This may be a long shot. My place of residency is Delaware. My wife works in DE and children are in school. My wife and I have a lease and expences there. In July, I took on a new job that is in NYC. The cost to take the Amtrak was to high for daily commute. So I decided to rent an apartment in NJ close to NYC and communte to Delaware every other weekend. I cover all my rental and expenses and pay for all the utilities in Delaware too. Is it possible to deduct any of the out of state expenses I.e rent , utilities? Though salary is better in NYC, the cost of living has begun to outweigh the salary benefit. The plan is to see how job turns out in one year then move the family to NJ if all goes well with new job. Thanks!

Since your intent is that your NY job is long term (it's not a short term assignment), you may not deduct travel or living expenses.

BTW - you say "my place of residency is Delaware" - but that's not correct. For tax purposes your place of residency (your "principal abode") is in NJ, even though you lease property in DE and your family resides there. So while you don't mention it - you do plan to file a resident tax return with NJ and a non-resident return with NY, correct?