Had an adverse possession situation. Bought the property, neighbor claimed prior consent w/ previous owner. Have attorney in family, but still required thousands $ to resolve. Repeated law enforcement complaints can bolster the claim of ownership, Suggest having a survey performed, then file an action in municipal small claims court. Judge reluctant to rule without a recent survey. Bring copies of verified police complaints. Photos even video of tresspass helpful in court. We sued in a superior court but not necessary..
Defendent in our case was somewhat unbalanced. Sometime an act, never know for sure, but wasn't willing to concede land while offering no legal resistance!! A favorable court decision stops the clock on possession, NY Law, I believe is 7 years, unimpeaded access.
EDIT: sheriff can NOT refuse service. Go to the sheriff himself, not an underling, unless he would prefer to forgo reelection. If it were a trespass related to hunting, fishing, trapping then I agree w/ DEC jurisdiction. But tresspass, even AG trepass , is a criminal violation, sheriff has responsibility to enforce every law written in penal code. It is your choice to seek trespass remedy/ relief under enviornmental law, but not required.