Third conditionals with talking about the abilities

I know how to construct third conditionals and mixed conditionals. However, recently I come across a situation in which I had to talk about what if could have done something in the past, what I would have done. In actual fact, I cannot ask this question with precise grammar. Simply, what I need to ask is how can I talk about things that I could have done in the past and what would be the possible results in the past. I mean, when we talk about past hypothetical situations, we often use "if + sb + had + past participle". But the thing is how can I tell about abilities I mean is it feasible to say "if I could had completed it".

Is following sentence is correct?

If I could had completed the task in advance, I would have been free yesterday.