How to confirm custom transaction with solo mining?
In Bitcoin, it is the miners' task to order the transactions. Thus, it is possible for a miner to pick which transactions they want to confirm. By default, they pick the ones that will provide the largest mining revenue to them, but often they will pick transactions to prioritize out of band.

However, you can only confirm a transaction by mining a block. That's what a confirmation is, a transaction being included in a block and thus being committed to on the blockchain.

However, it is infeasible for you to mine a block at home. Whatever minig power you may be able to acquire and run at home will likely not help you mine a single block in the next 1,000 years. I've elaborated here: In the ASIC-age, is it worth starting mining Bitcoin at home?