How long does abiological parent have to not be in contact with or about their minor child before it is cosidered abandonment in the state of Georgia?

Generally speaking it is a full year. But this means no contact, no birthday cards, no support payments, no anything. However, you can't just file abandonment. Abandonment can be used as grounds for something else like a TPR but those are hard to get. Perhaps if you tell us what you are trying to accomplish with abandonment we can tell you a way to get it.