I own a home and live in the home that has a second apt. The tenants never fulfilled the deposit agreement. They were to switch utilities by December 1st which they have not done, but they were suppose to pay utilites kept in our name from Sept 1 to Dec 1 which they have not done. They have not paid rent for December and told us they have no intention of doing so. They also said they are not leaving when I gave them 3 day eviction for violation of agreement and non-payment.

Did you given them a written eviction? I take it you know your state law is three day notice.
When they do not leave in three days go to court and file for a court eviction. Then when that is up the Constable or sheriff will be sent out to remove them.
After they are out you can go after them for a judgment against them for what they owe.

I am in NY but to be honest I fear my safety and get something , huh! No way, they owe their last landlord 3000 for utilites we found out. And they owe the IRS 151,000 so don't think I will get any judgement paid... so more of my money gone...

Even if you don't get judgment paid it will go on their record and make their credit worse and that will be warning to anybody that checks their credit.