ESP8266 in Both Mode AccesssPoint and Station mode, you can connect with esp8266 using your mobile and your ESP8266 connects to your another wifi connection(Home router,) both mode work simultaneously

blog_esp8266_series_AP_STA.ino

/*
  OUTCOME: Esp8266 Hotspot as well as Connecting your Esp8266 to any Wifi NETWORK(Mobile Hotspot,Home Route) 
  Author: Ankit Rana (Futechiot)
  Board Used: Wemos d1 mini, Wemos d1 mini pro, Node MCU

  Website: www.futechiot.com
  GitHub: https://github.com/futechiot

  Software:
  Advanced IP Scanner: https://www.advanced-ip-scanner.com/

  -->download and open this application
  -->Scan for networks, make sure your PC and board are connected in same network
  -->search for obtained IP, see in manufracturer "ESPRESSIF"

  --> Scan for wifi in your mobile or laptop you will see your hotspot name in scanned network

*/


#include <ESP8266WiFi.h>               //Wifi library of esp8266 to access HARDWARRE APIS and othe functionality

/* Set these to your Wifi credentials. */

const char*Wifi_ssid = "INCORE_AP_IoT";                             // SSID of your Router OR mobile hotspot
const char*Wifi_password = "Welcome@Incore";                       //  PASSWORD of your Router or Mobile hotspot see below example

const char *Apssid = "WHAT EVER YOU LIKE";                      //give Accesspoint SSID, your esp's hotspot name 
const char *Appassword = "PASSWORD";                           //password of your esp's hotspot

void setup() {

  // put your setup code here, to run once:

  Serial.begin(115200);               //to enable Serial Commmunication with connected esp8266 board
  delay(500);
  WiFi.mode(WIFI_AP_STA);           //changing ESP9266 wifi mode to AP + STATION

  WiFi.softAP(Apssid, Appassword);         //Starting AccessPoint on given credential
  IPAddress myIP = WiFi.softAPIP();        //IP Address of our Esp8266 accesspoint(where we can host webpages, and see data)
  Serial.print("Access Point IP address: ");
  Serial.println(myIP);
  
  Serial.println("");

  delay(1500);
  Serial.println("connecting to Wifi:");
  Serial.println(Wifi_ssid);

  WiFi.begin(Wifi_ssid, Wifi_password);                  // to tell ESP8266 Where to connect and trying to connect
  while (WiFi.status() != WL_CONNECTED) {                // While loop for checking Internet Connected or not
    delay(500);
    Serial.print(".");
  }

  Serial.println("");
  Serial.println("WiFi connected");
  Serial.println("IP address: ");
  Serial.println(WiFi.localIP());            // successful Connection of ESP8266,
                                            // printing Local IP given by your Router or Mobile Hotspot,
                                           // Esp8266 connect at this IP

  Serial.println("");

}

void loop() {
  // put your main code here, to run repeatedly:

}

Thank you! I have implemented this + elegantOTA + arduinoOTA so I have full flexibility to update my esp8266

Thank you, works without any problem.