My Father died like 15 or 16 years ago, he was my grandfather but he adopted me when I was a baby. He served in the US Army but he deserted from war, my mother (grandmother) still receives benefis from social security since my father died. My question is That becomes me an US citizen or can I appy for an immigration process?

If you're legally adopted, you are US citizen.. but this is not 100% as I need more info... date and all relevant documents.