I completed my 2nd year of BE course and had a gap of 3 years after that due to financial reasons. Can I continue 3rd year in same college?

Yes , like you can continue your BE course after a 3-year gap, but it usually  depends upon  college's policies. you should first Contact your college to inquire about re-admission, as some colleges require documentation explaining the gap (e.g., financial reasons,etc) and proof of good previous aca