USBasp using correct driver (libusbk 3.0.7.0) and windows 10. Device manager shows all ok with USBasp listed in libusbk folder.
Simple hookup to tiny85 via homemade pcb.
USBasp software is original version by Fischer. Have also tried with chinese clone version which come up with cannot set speed warning as per usual. Have link on programmer for slow speed (JP3) but it makes no difference on or off.
Settings as per picture.
Bootloader appears to work fine, no errors just comes up with - Done burning bootloader. This implies correct connection of pins to USBasp or it would show an error.
Trying to upload by programmer gives :-
Resetting the board
Failed to reset the board, upload failed
An error occurred while uploading the sketch
Arduino version 1.8.12.
I have two boards to program one with the dip version and the other with a SMT version. Both behave identically.
I don't mind if the bootloader stays or goes as the program is very small.
This won't help, but I have the verry same problem. I even tried the STM32-versn of usbisp. Working or not is not consistent over target boards: some targets work, some don't. AVR-ISPMkII et. al. work perfectly fine.
I'm using the USBAsp programmer a lot - never for the ATtiny85, but so far working perfectly for several ATtiny84, ATmega328PB, and ATmega1284 projects.
Without schematic not much to be said about your problem. It is odd that the burning of the bootloader apparently goes without a hitch.
I do remember having a really hard time getting the correct driver on my Windows laptop. On the other hand, on my Linux desktop it just worked out of the box. Windows continues to be a struggle to get and keep things working...