First you will need to file a claim for disability compensation that shows the added disability occurred while receiving VA medical care or through a VA program designed to help vets find work.
I'd like to know if am I qualified to apply for a disability benefits from VA if I had a surgery which is linked to an injury I sustained while serving in the military?
In that case, you are going to need that the surgery required a recovery time of at least one month or reports show that the surgery or treatment was for a service-connected disability.