I was taxed for small earning from options trading last 12/28 but the value of that stock dropped and I am now at a loss. Can I recover the tax there?

If the stock dropped in value in 2022 and you have not yet sold that stock, then it is an unrealized loss and you cannot deduct that loss in 2021, or recover the tax you paid on the gain on options in 2021.

You can deduct capital losses only when you sell the stock at a loss.