Is it possible to connect USB printer to Atmega8
USB is a particularly complex and timing-sensitive protocol which is not conducive to bit-banging on a microcontroller. Even attempting to manually implement the USB state machine in an FPGA from the ground up would be a significant amount of work, involving deep knowledge of the USB specification and practical implementation quirks.

You'll need an external USB host IC, or a microcontroller with inbuilt USB host support.