I'm trying to do an electronic testimony can I do that here in Florida with a New York case? I just moved here 3 months ago

If you have a case in NY, it is up to the court there to decide whether or not you can appear electronically (via phone, Skype, FaceTime,...). There is no FL law that allows or prohibits what you want to do.

This is issue is genuinely one that depends on the judge that has the case in New York. In Florida, the courts have become very comfortable with the use of technology that permits witnesses to testify from outside the court's jurisdiction. I am sure the same can be said of New York. However, your situation may be a bit different. I am assuming that you are a litigant before the New York courts. If that is the case, your presence may be indispensable. If you have a lawyer in NY, I would consult with him/her as soon as possible so a motion may be filed. If you don't have a lawyer, then send a letter to the judge, with a copy to all of the parties, asking permission to appear by telephone and/or videophone.

If you are considering appearing in the NY case from Florida and the issue is alimony or support you may be able to appear by written document, telephone, etc under the UIFSA rules that have been enacted in almost all of the states in the US. NY definitely has a version. You must file a petition/registration depending on what you want to accomplish and the related necessary documents which you can find on the internet at the following site http://www.acf.hhs.gov/programs/css/resource-library/search?keyword=interstate%20forms&h=1#?keyword[0]=interstate%20forms&area[2682]=2682&ajax=1. The statutes in almost all states indicate that the court can't make you appear and must find an alternative to your physical presence. It may not be the method of appearance you want however. If the issue is child support the local CSE office is supposed to make it possible for you to appear even if you have not requested their services (at least a few years ago that was true). It will take talking to a Supervisor to accomplish if you go that route. UIFSA is available to both private individuals as well as the agency responsible for Child Support.