Photoshop script that saves the whole document for each top level layer inside the selected group.

Export document for each layer inside selected group.jsx

// Name: Export document for each layer inside selected group.jsx
// Formerly: Export Layers Inside Selected Group.jsx

// Description: Photoshop script that saves the whole document for each top level layer inside the selected group.
// Image example: https://user-images.githubusercontent.com/1164476/49152494-aef8af00-f31b-11e8-80ff-d774e3103eae.png

// https://gist.github.com/joonaspaakko/013a223e94ba0fb9a2a0

#target photoshop

try {
  var doc = app.activeDocument;
	var n = 0;
	var duplicates = {};
}
catch (e) {
  alert( 'Open a document first...' );
}

function processLayers( options) {
	
	var group       = doc.activeLayer;
	var groupLength = group.layers.length;
	
	var visibleArray = [];
	
	// HIDE ALL LAYERS
	for ( var i = 0; i < groupLength; i++ ) {
		visibleArray.push( group.layers[i].visible );
		group.layers[i].visible = false;
	}
	
	// START SAVING
	options.docName = doc.name.split('.')[0]; // Assumes filename contains only one period before the extion.
	for ( var i = 0; i < groupLength; i++ ) {
		
		var layer = group.layers[ i ];
		
		options.layerName = layer.name;
		options.layerIndex = i+1;
		
		layer.visible = true;
		save.file( options );
		layer.visible = false;
		
	}
	
	// RESTORE VISIBILITY
	for ( var i = 0; i < groupLength; i++ ) {
		group.layers[i].visible = visibleArray[i];
	}
	
	doc.activeLayer = group;

	alert('Done!'); // There's no error check so who am I to say if the files were saved, but at least the script is done...
	
}

var save = {
	file: function( options ) {
		
		var saveOptions = {};
		
		for ( var i=0; i < options.fileFormats.length; i++ ) {
			
			var fileformat = options.fileFormats[i];
			var destinationFolder = options.destination + "/" + fileformat.toUpperCase();
			
			makeFolder( destinationFolder ); // If it doesn't exist already...
			
			var filename = '';
			filename += options.prefix;
			filename += options.useLayerName ? options.layerName : options.custonName;
			filename += options.suffix;
			
			// IF FILENAME CONTAINS A DOLLAR SIGN
			if ( filename.match(/\$/) !== null ) {
				filename =  filename.replace('$',options.layerIndex);
			}
			// IF FILENAME DOESN'T HAVE THE DOLLAR SIGN AND A
			// DUPLICATE FILENAME IS FOUND, ADD A NUMBER ANYWAYS.
			else {
				
				if ( typeof duplicates[ fileformat ] == 'undefined' ) {
					duplicates[ fileformat ] = {};
				}
				
				var duplicateNumber = '';
				if ( typeof duplicates[ fileformat ][ filename ] === 'object' ) {
					duplicateNumber = ' ' + duplicates[ fileformat ][ filename ].length;
					duplicates[ fileformat ][ filename ].push( filename );
				}
				else {
					duplicates[ fileformat ][ filename ] = [ filename ];
				}
				
				filename += duplicateNumber;
			}
			
			doc.saveAs( File( destinationFolder + "/" + filename ), save[ fileformat ](), true );
			
		}
		
	},
	psd: function() {
		
		var psd_saveOpts = new PhotoshopSaveOptions();
		
		psd_saveOpts.layers            = true;
		psd_saveOpts.embedColorProfile = true;
		psd_saveOpts.annotations       = true;
		psd_saveOpts.alphaChannels     = true;
		
		return psd_saveOpts;
		
	},
	pdf: function() {
		
		var presetName = '[High Quality Print]';
		
		var pdf_SaveOpts = new PDFSaveOptions();
		
		pdf_SaveOpts.pDFPreset = presetName;
		
		return pdf_SaveOpts;
		
	},
	jpeg: function() {
		
		var jpg_SaveOpts = new JPEGSaveOptions();
		
		jpg_SaveOpts.matte   = MatteType.WHITE;
		jpg_SaveOpts.quality = 10;
		jpg_SaveOpts.formatOptions.STANDARDBASELINE;
		
		return jpg_SaveOpts;
		
	},
	png: function() {
		
		var png_SaveOpts = new PNGSaveOptions();
		
		png_SaveOpts.compression = 9;
		png_SaveOpts.interlaced = false;
		
		return png_SaveOpts;
		
	},
	tiff: function() {
		
		var tiff_SaveOpts = new TiffSaveOptions();
		
		tiff_SaveOpts.alphaChannels      = true;
		tiff_SaveOpts.annotations        = true;
		tiff_SaveOpts.imageCompression   = TIFFEncoding.JPEG;
		tiff_SaveOpts.interleaveChannels = true;
		tiff_SaveOpts.jpegQuality        = 10;
		tiff_SaveOpts.layers             = true;
		tiff_SaveOpts.layerCompression   = LayerCompression.ZIP;
		tiff_SaveOpts.transparency       = true;
		
		return tiff_SaveOpts;
		
	}
};

function makeFolder( path ) {
  var newFolder = Folder( path );
  if( !newFolder.exists ) newFolder.create();
}

if ( app.documents.length > 0 ) {
  if ( app.activeDocument.activeLayer.layers ) {
		init();
  }
  else {
    alert( "Error: \nSelect a parent group of the layers you want to export.")
  }
}

function init() {
	
	/*
	Code for Import https://scriptui.joonas.me — (Triple click to select):
	{"items":{"item-0":{"id":0,"type":"Dialog","parentId":false,"style":{"text":"Export document for each layer inside selected group.jsx","preferredSize":[0,0],"margins":16,"orientation":"column","spacing":10,"alignChildren":["center","top"]}},"item-1":{"id":1,"type":"Checkbox","parentId":6,"style":{"text":"PSD","preferredSize":[0,0],"alignment":null}},"item-2":{"id":2,"type":"Checkbox","parentId":6,"style":{"text":"TIFF","preferredSize":[0,0],"alignment":null}},"item-3":{"id":3,"type":"Checkbox","parentId":6,"style":{"text":"JPEG","preferredSize":[0,0],"alignment":null,"checked":true}},"item-4":{"id":4,"type":"Checkbox","parentId":6,"style":{"text":"PNG","preferredSize":[0,0],"alignment":null}},"item-5":{"id":5,"type":"Checkbox","parentId":6,"style":{"text":"PDF","preferredSize":[0,0],"alignment":null}},"item-6":{"id":6,"type":"Panel","parentId":9,"style":{"text":"","preferredSize":[0,0],"margins":10,"orientation":"row","spacing":10,"alignChildren":["center","top"],"alignment":null}},"item-7":{"id":7,"type":"Panel","parentId":9,"style":{"text":"","preferredSize":[0,0],"margins":10,"orientation":"column","spacing":10,"alignChildren":["left","top"],"alignment":null}},"item-8":{"id":8,"type":"EditText","parentId":14,"style":{"text":"","preferredSize":[90,0],"alignment":null}},"item-9":{"id":9,"type":"Group","parentId":0,"style":{"preferredSize":[0,0],"margins":0,"orientation":"column","spacing":10,"alignChildren":["fill","top"],"alignment":null}},"item-10":{"id":10,"type":"Group","parentId":0,"style":{"preferredSize":[0,0],"margins":[15,0,10,0],"orientation":"row","spacing":10,"alignChildren":["left","top"],"alignment":null}},"item-11":{"id":11,"type":"Button","parentId":10,"style":{"text":"Save","justify":"center","preferredSize":[0,0],"alignment":null}},"item-12":{"id":12,"type":"Button","parentId":10,"style":{"text":"Cancel","justify":"center","preferredSize":[0,0],"alignment":null}},"item-13":{"id":13,"type":"StaticText","parentId":14,"style":{"text":"Prefix:","justify":"left","preferredSize":[0,0],"alignment":null}},"item-14":{"id":14,"type":"Group","parentId":22,"style":{"preferredSize":[0,0],"margins":0,"orientation":"column","spacing":10,"alignChildren":["left","top"],"alignment":null}},"item-15":{"id":15,"type":"Checkbox","parentId":7,"style":{"text":"Use layer name","preferredSize":[0,0],"alignment":null,"checked":false}},"item-16":{"id":16,"type":"Group","parentId":22,"style":{"preferredSize":[0,0],"margins":0,"orientation":"column","spacing":10,"alignChildren":["left","top"],"alignment":null}},"item-17":{"id":17,"type":"StaticText","parentId":16,"style":{"text":"Custom name:","justify":"left","preferredSize":[0,0],"alignment":null}},"item-18":{"id":18,"type":"EditText","parentId":16,"style":{"text":"File Name ","preferredSize":[160,0],"alignment":null}},"item-19":{"id":19,"type":"Group","parentId":22,"style":{"preferredSize":[0,0],"margins":0,"orientation":"column","spacing":10,"alignChildren":["left","top"],"alignment":null}},"item-20":{"id":20,"type":"StaticText","parentId":19,"style":{"text":"Suffix:","justify":"left","preferredSize":[0,0],"alignment":null}},"item-21":{"id":21,"type":"EditText","parentId":19,"style":{"text":"","preferredSize":[90,0],"alignment":null}},"item-22":{"id":22,"type":"Group","parentId":7,"style":{"preferredSize":[0,0],"margins":0,"orientation":"row","spacing":10,"alignChildren":["left","center"],"alignment":null}},"item-23":{"id":23,"type":"Divider","parentId":7,"style":false},"item-24":{"id":24,"type":"StaticText","parentId":7,"style":{"text":"Dollar symbol ($) is replaced with incremental numbers","justify":"left","preferredSize":[0,0],"alignment":"center"}}},"order":[0,9,7,15,23,22,14,13,8,16,17,18,19,20,21,24,6,3,4,1,5,2,10,12,11],"activeId":10}
	*/

	// DIALOG
	// ======
	var dialog = new Window("dialog");
	    dialog.text = "Export document for each layer inside selected group.jsx";
	    dialog.orientation = "column";
	    dialog.alignChildren = ["center","top"];
	    dialog.spacing = 10;
	    dialog.margins = 16;

	// GROUP1
	// ======
	var group1 = dialog.add("group");
	    group1.orientation = "column";
	    group1.alignChildren = ["fill","top"];
	    group1.spacing = 10;
	    group1.margins = 0;

	// PANEL1
	// ======
	var panel1 = group1.add("panel");
	    panel1.orientation = "column";
	    panel1.alignChildren = ["left","top"];
	    panel1.spacing = 10;
	    panel1.margins = 10;

	var checkbox1 = panel1.add("checkbox");
	    checkbox1.text = "Use layer name";

	var divider1 = panel1.add("panel");
	    divider1.alignment = "fill";

	// GROUP2
	// ======
	var group2 = panel1.add("group");
	    group2.orientation = "row";
	    group2.alignChildren = ["left","center"];
	    group2.spacing = 10;
	    group2.margins = 0;

	// GROUP3
	// ======
	var group3 = group2.add("group");
	    group3.orientation = "column";
	    group3.alignChildren = ["left","top"];
	    group3.spacing = 10;
	    group3.margins = 0;

	var statictext1 = group3.add("statictext");
	    statictext1.text = "Prefix:";

	var edittext1 = group3.add("edittext");
	    edittext1.minimumSize.width = 90;

	// GROUP4
	// ======
	var group4 = group2.add("group");
	    group4.orientation = "column";
	    group4.alignChildren = ["left","top"];
	    group4.spacing = 10;
	    group4.margins = 0;

	var statictext2 = group4.add("statictext");
	    statictext2.text = "Custom name:";

	var edittext2 = group4.add("edittext");
	    edittext2.text = "File Name ";
	    edittext2.minimumSize.width = 160;

	// GROUP5
	// ======
	var group5 = group2.add("group");
	    group5.orientation = "column";
	    group5.alignChildren = ["left","top"];
	    group5.spacing = 10;
	    group5.margins = 0;

	var statictext3 = group5.add("statictext");
	    statictext3.text = "Suffix:";

	var edittext3 = group5.add("edittext");
	    edittext3.minimumSize.width = 90;

	// PANEL1
	// ======
	var statictext4 = panel1.add("statictext");
	    statictext4.text = "Dollar symbol ($) is replaced with incremental numbers";
	    statictext4.alignment = ["center","top"];

	// PANEL2
	// ======
	var panel2 = group1.add("panel");
	    panel2.orientation = "row";
	    panel2.alignChildren = ["center","top"];
	    panel2.spacing = 10;
	    panel2.margins = 10;

	var checkbox2 = panel2.add("checkbox");
	    checkbox2.text = "JPEG";
	    checkbox2.value = true;

	var checkbox3 = panel2.add("checkbox");
	    checkbox3.text = "PNG";

	var checkbox4 = panel2.add("checkbox");
	    checkbox4.text = "PSD";

	var checkbox5 = panel2.add("checkbox");
	    checkbox5.text = "PDF";

	var checkbox6 = panel2.add("checkbox");
	    checkbox6.text = "TIFF";

	// GROUP6
	// ======
	var group6 = dialog.add("group");
	    group6.orientation = "row";
	    group6.alignChildren = ["left","top"];
	    group6.spacing = 10;
	    group6.margins = [0,15,0,10];

	var button1 = group6.add("button", undefined, undefined, {name:"cancel"});
	    button1.text = "Cancel";
	    button1.justify = "center";

	var button2 = group6.add("button", undefined, undefined, {name:"ok"});
	    button2.text = "Save";
	    button2.justify = "center";
  
	
	// DIALOG CUSTOMIZATION
	var filename = edittext2;
	filename.text = app.activeDocument.name.split()[0]; // Assumes filename contains only one period before the extion.
	filename.active = true;
	
  var useLayerName = checkbox1;
  useLayerName.onClick = function() {
    var check = this.value;
    var customName = edittext2;
    if ( check ) customName.enabled = !check;
    else customName.enabled = !check;
  };
  
  var cancelBtn = button1;
  cancelBtn.onClick = function() {
		dialog.close();
  };
  
  var saveBtn = button2;
  saveBtn.onClick = function() {
		n = ++n;
		if ( n === 1 ) {
			
	    var formatsArray = [];
	    var formats = panel2.children;
	    for (var i = 0; i < formats.length; i++) {
				var format = formats[i];
				if ( format.value ) {
					formatsArray.push( format.text.toLowerCase() );
				}
	    }
			
			var path = '';
			try { path = doc.path; } catch(e) {}
			
	    var options = {
	      useLayerName: useLayerName.value,
	      fileFormats: formatsArray,
	      prefix: edittext1.text,
	      custonName: edittext2.text,
	      suffix: edittext3.text,
				destination: Folder.selectDialog( 'Select destination folder...', path )
	    };
	    
	    dialog.close();
	    
			if ( options.destination ) {
				processLayers( options );
			}
			
		}
  };
	
	dialog.show();
	
}

Updated the script with a few new features:

• Use layer name
• Prefix
• Suffix