What is the maximum amount of time i have or deadline to file an amended tax return for the 2013 tax year? 2014?

There's no deadline to file an original return or submit an amendment to fix a mistake on a previously filed tax return. You can always file an old return or fix a mistake.

However, if you are claiming a refund then it must be submitted within 3 years of the original deadline. For 2013 returns were "due" on April 15th 2014, so the 3 year window allows you to claim a refund until April 15th 2017.

Technically you can file a return or amendment after that date, but you won't receive a refund and if you've gone that long without the IRS catching a mistake then its highly unlikely they would initiate an audit or investigation so there'd be no reason to file

you can amend any tax return you feel needs to be done, the point is if you think you are due a refund they are no longer available to be remitted to you if you do not file the amendment by the third anniversary date of the filing of your amendment for 2013 would be after 4/15/2017

You have until next April 15 if you are looking for a refund based on withholding. If you have made payments on delinquent tax since then it is two years from the date of payments for those.

Forever. And get a refund? 3 years form original due date.

No Greg. I am asking about filing, not getting audited. Goodbye.

They can audit or charge you anytime you want to. The longer you wait, the more likely.