Atmega168P AU (SMD) Bootloading fail

I am using standard bootloader circuit having 16Mhz oscillator with two 22pf capacitors connected and one 10k resistor with reset (I'll attach my circuit diagram if needed). I am using USB ASP AVR Programmer. I can successfully bootload atmega328p au chip with my current circuit but not atmega168p au. With Atmega328p au I am setting

board > "Arduino pro or pro mini" and processor > "Atmega328P (16MHz and 5V)"

in arduino ide. When using it with 168 I am configuring above setting as

board > "Arduino pro or pro mini" and processor > "Atmega168P (16MHz and 5V)"

but in this case its not working. It gives error

avrdude: Expected signature for ATmega168 is 1E 94 06
Double check chip, or use -F to override this check.
Error while burning bootloader.

Any help would be appreciated.

Turn on verbose uploading (in preferences) and quote more of the resulting errors. (in part6icular, what signature is it seeing?)

The pro-mini doesn't have an ATmega168P. It only has an ATmega168 (the chips are nearly indistinguishable, but they do have different signatures.)

Thanks for reply. Yes its showing that device signature is 168p and i am trying to bootload 168 configuration. Verbose attached below:-

Arduino: 1.8.9 (Windows Store 1.8.21.0) (Windows 10), Board: "Arduino Pro or Pro Mini, ATmega168 (5V, 16 MHz)"

C:\Program Files\WindowsApps\ArduinoLLC.ArduinoIDE_1.8.21.0_x86__mdqgnx93n4wtt\hardware\tools\avr/bin/avrdude -CC:\Program Files\WindowsApps\ArduinoLLC.ArduinoIDE_1.8.21.0_x86__mdqgnx93n4wtt\hardware\tools\avr/etc/avrdude.conf -v -patmega168 -cusbasp -Pusb -e -Ulock:w:0x3F:m -Uefuse:w:0xF8:m -Uhfuse:w:0xdd:m -Ulfuse:w:0xff:m 

avrdude: Version 6.3-20171130
         Copyright (c) 2000-2005 Brian Dean, http://www.bdmicro.com/
         Copyright (c) 2007-2014 Joerg Wunsch

         System wide configuration file is "C:\Program Files\WindowsApps\ArduinoLLC.ArduinoIDE_1.8.21.0_x86__mdqgnx93n4wtt\hardware\tools\avr/etc/avrdude.conf"

         Using Port                    : usb
         Using Programmer              : usbasp
         AVR Part                      : ATmega168
         Chip Erase delay              : 9000 us
         PAGEL                         : PD7
         BS2                           : PC2
         RESET disposition             : dedicated
         RETRY pulse                   : SCK
         serial program mode           : yes
         parallel program mode         : yes
         Timeout                       : 200
         StabDelay                     : 100
         CmdexeDelay                   : 25
         SyncLoops                     : 32
         ByteDelay                     : 0
         PollIndex                     : 3
         PollValue                     : 0x53
         Memory Detail                 :

                                  Block Poll               Page                       Polled
           Memory Type Mode Delay Size  Indx Paged  Size   Size #Pages MinW  MaxW   ReadBack
           ----------- ---- ----- ----- ---- ------ ------ ---- ------ ----- ----- ---------
           eeprom        65    20     4    0 no        512    4      0  3600  3600 0xff 0xff
           flash         65     6   128    0 yes     16384  128    128  4500  4500 0xff 0xff
           lfuse          0     0     0    0 no          1    0      0  4500  4500 0x00 0x00
           hfuse          0     0     0    0 no          1    0      0  4500  4500 0x00 0x00
           efuse          0     0     0    0 no          1    0      0  4500  4500 0x00 0x00
           lock           0     0     0    0 no          1    0      0  4500  4500 0x00 0x00
           calibration    0     0     0    0 no          1    0      0     0     0 0x00 0x00
           signature      0     0     0    0 no          3    0      0     0     0 0x00 0x00

         Programmer Type : usbasp
         Description     : USBasp, http://www.fischl.de/usbasp/

avrdude: auto set sck period (because given equals null)
avrdude: warning: cannot set sck period. please check for usbasp firmware update.
avrdude: AVR device initialized and ready to accept instructions

Error while burning bootloader.
Reading | ################################################## | 100% 0.00s

avrdude: Device signature = 0x1e940b (probably m168p)
avrdude: Expected signature for ATmega168 is 1E 94 06
         Double check chip, or use -F to override this check.

avrdude done.  Thank you.

So what board and processor should I choose for this chip?

The easiest thing to do would be to install "minicore", which has an additional pull-down menu to support the ATmega168P.

Minicore worked!. Thanks a lot for help. Just One more question. I can compile and upload blink code for this board configuration (using minicore), but when i tried my previous code (that i was using with Atmega328p) which has

#include <TimerOne.h>

It gives error:-

C:\Users\Ultron\Documents\Arduino\libraries\TimerOne/TimerOne.h: In member function 'void TimerOne::setPwmDuty(char, unsigned int)':

C:\Users\Ultron\Documents\Arduino\libraries\TimerOne/TimerOne.h:105:13: error: 'TIMER1_A_PIN' was not declared in this scope

  if (pin == TIMER1_A_PIN) OCR1A = dutyCycle;

             ^

exit status 1
Error compiling for board ATmega168.