How to use an SSD1603 (oled 0.96'') with Attiny85

Please post a link to the actual display that you have bought. e.g. Ebay sale.

Or post a clear photo of the pcb.

3W_SW_SPI generally means 9-bit SPI with no DC pin.
4W_SW_SPI or 4W_HW_SPI means 8-bit SPI with a DC pin

As a general rule, every SPI device should have a CS pin. Or you can never have other devices on the same SPI bus.

Oliver recommends using U8g2.
I suggest that you try:

U8G2_SSD1306_128X64_NONAME_1_4W_SW_SPI(rotation, clock, data, cs, dc [, reset])

with a dummy argument for CS.

However, we can give a sensible answer if/when we can see the pcb

David.