ESP8266 and RC522 can't work together

I am having problem with the ESP8266 and RC522 on Arduino uno
IF the Arduino reset pin connect to the ground, the ESP work fine but RC522 not.
IF the reset pin doesn't connect, the RC522 work but the ESP not
Is the circuit connection wrong or the code need some change?

#include <ESP8266WiFi.h>
#include <WiFiClientSecure.h>
#include <ESP8266WebServer.h>
#include <ESP8266HTTPClient.h>
#include <SPI.h>
#include <MFRC522.h> 
#define RESET   9
#define SS      10
MFRC522 mfrc522(SS, RESET); 


/* Set these to your desired credentials. */
const char *ssid = "tai";  //ENTER YOUR WIFI SETTINGS
const char *password = "264395361";
String day;
String time2;
String time1;
int pos;
String hour;
String linkurl;
String linkurl2;

//Link to read data from https://jsonplaceholder.typicode.com/comments?postId=7
//Web/Server address to read/write from
const char *host = "test3-xxxxx.firebaseio.com";
const int httpsPort = 443;  //HTTPS= 443 and HTTP = 80


//SHA1 finger print of certificate use web browser to view and copy
const char fingerprint[] PROGMEM = "x";
//=======================================================================
//                    Power on setup
//=======================================================================




int rfid(){
  int stid=0;
  if (mfrc522.PICC_IsNewCardPresent()) {
    if (mfrc522.PICC_ReadCardSerial()){
      byte *id = mfrc522.uid.uidByte;
      byte idSize = mfrc522.uid.size;
      for (byte i = 0; i < idSize; i++) {
        Serial.print("0x");
        Serial.print(id[i]);
        Serial.print(" ");

      }
       stid=int(id[0])+int(id[1])+int(id[2])+int(id[3]);
       Serial.println();
       Serial.print(stid);
       return stid;
      Serial.println();

    }
    mfrc522.PICC_HaltA();
  }

}


String GETTIME() {
  String payload;
  HTTPClient http;  //Declare an object of class HTTPClient

  http.begin("http://worldtimeapi.org/api/ip");  //Specify request destination
  int httpCode = http.GET();                                    //Send the request

  if (httpCode > 0) { //Check the returning code

    payload = http.getString();   //Get the request response payload
    Serial.println(payload);                     //Print the response payload

  }

  http.end();   //Close connection

  return payload;

}






void setup() {
  delay(1000);
  Serial.begin(115200);
  SPI.begin();      // Init SPI bus
  mfrc522.PCD_Init();   // Init MFRC522
  delay(4);       // Optional delay. Some board do need more time after init to be ready, see Readme
  mfrc522.PCD_DumpVersionToSerial();  // Show details of PCD - MFRC522 Card Reader details
  Serial.println(F("Scan PICC to see UID, SAK, type, and data blocks..."));




  
  WiFi.mode(WIFI_OFF);        //Prevents reconnection issue (taking too long to connect)
  delay(1000);
  WiFi.mode(WIFI_STA);        //Only Station No AP, This line hides the viewing of ESP as wifi hotspot

  WiFi.begin(ssid, password);     //Connect to your WiFi router
  Serial.println("");

  Serial.print("Connecting");
  // Wait for connection
  while (WiFi.status() != WL_CONNECTED) {
    delay(500);
    Serial.print(".");
  }

  //If connection successful show IP address in serial monitor
  Serial.println("");
  Serial.print("Connected to ");
  Serial.println(ssid);
  Serial.print("IP address: ");
  Serial.println(WiFi.localIP());  //IP address assigned to your ESP


  
  
}






//=======================================================================
//                    Main Program Loop
//=======================================================================
void loop() {
 
  time1 = GETTIME();
  
  
  int sum=rfid();
  Serial.println(sum);
  

  
  //PATCH();


  delay(2000);  //POST Data at every 2 seconds

}

When reset of the Uno is connected to ground it stops the Uno microcontroller from working so you can program the ESP-01 via the Uno's USB/serial adaptor but the ESP-01 is being powered from the Uno 3.3v pin and this cannot deliver enough current to ensure the ESP-01 keeps powered.

I would suggest you invest in a different ESP8266 module like this or this so you can connect the RC522 directly to the ESP8266 and remove the need of the Uno.

There are probably several different versions of the RC522 but the first one I looked at (to confirm what it was) says it's a 3.3V but the SPI of the UNO is 5V so you may have damaged the RC522.

ESP8266 and RC522 on Arduino uno

What code are you using for the Uno ? You can only have 1 device communicating on the Serial port at one time. I think you would make life a lot easier on yourself if you would use an ESP that does have SPI, like a nodeMCU.
The code you show is for the ESP (doesn't compile for an UNO) but

#define RESET   9
#define SS      10
MFRC522 mfrc522(SS, RESET);

these pins are not connected on the ESP-01.

but the ESP-01 is being powered from the Uno 3.3v pin and this cannot deliver enough current to ensure the ESP-01 keeps powered

That should actually be OK if it is an original UNO, but only just.