I use Arduino Nano as programmer and I have absolutely no problems with Attiny 85 that I bought from Digikey.
I have a couple of Attiny 85 that I bought from Aliexpress that I can’t program. When I try to program them I get this message:
avrdude: Yikes! Invalid device signature.
Double check connections and try again, or use -F to override this check.
I tried to burn bootlogger and I also tried an external clock with 85 but I got the same message.
Once I replace Aliexperss 85 with the one that one that I got from Digikey everything works like charm.
As a side-note: If the AT85 is clocked at 1MHz (factory default) it may not respond to a fast programmer. I use the USBASP programmer and then I need to select the slow speed programming mode to set the speed to 8 or 16MHz, after which it becomes responsive to a fast programmer.
A while back I stopped to buy MCU's from Aliexpress, as the amount of fakes I received did not justify the little price difference anymore. I even received ATTiny13 that were completely different 8pin chips with a fake marking.