Can I run Ornith-1.0-35B-GGUF on an RTX 3060 12 GB?
No
Even its smallest file (Q4_K_M, 21.2 GB) is more than an RTX 3060 12 GB can hold (10.8 GB usable): it needs 2 of them.
Files and context on RTX 3060 12 GB
Each file of Ornith-1.0-35B-GGUF (and of GGUF versions the site has analyzed), and how much context fits next to it, with the context cache in 16-bit or 8-bit.