This shows how to add an argument to a field in graphql and use it in a resolver.

add-argument-to-graphql-field.php

add_filter( 'graphql_RootQuery_fields', function( $fields ) {

	if ( isset( $fields['posts'] ) ) {
		$args = is_array( $fields['posts']['args'] ) ? $fields['posts']['args'] : [];
		$args['myCustomArg'] = [
			'type' => 'String',
			'description' => __( 'This is a field that was added via a filter', 'your-textdomain' ),
		];
		$fields['posts']['args'] = $args;
	}

	return $fields;

}, 20 );

add_filter( 'graphql_connection_query_args', function( $args, AbstractConnectionResolver $connection_resolver ) {

	// here's the input args provided by the query
	$input_args = $connection_resolver->getArgs();

	if ( isset( $input_args['myCustomArg'] ) ) {
		$args['s'] = $input_args['myCustomArg'];
	}


	return $args;

}, 10, 2 );