as far as I know, there are no OTP versions of any AVR processors.
FLASH-style memory has been cheaper than OTP-style memory for a long time now. An OTP memory cell is essentially a UV-erasable ("EPROM") cell that doesn't let you expose it to UV for erasure. The UVEPROM The cheaper memory technology that you're thinking of is probably "mask programmed ROM" chips, where the code is actually implemented as a layer of the chip creation. This is used for some very large volume applications, but it much more complex in the manufacturing phase (you have to get a MASK and have it used during the chip manufacturing. Tens of thousands of dollars or more of NRE costs, assuming that the semiconductor manufacturer is willing to do it at all.
Atmel does have some OTP 8051-architecture chips based on flash technology. I believe that they're essentially normal flash-based chips with the "erase" function disabled somehow. While they're somewhat cheaper, I think the main idea is permanence-related, and they're only cheaper for marketing reasons.