Mutant Ninja Turtles Gaiden (or MNT Gaiden for short) is a TMNT-based fan-comic written and drawn by 'Tigerfog', and it first began back in 2004. The basis of this comic comes from multiple sources, but the main influences coming from Tigerfog herself are from the orignal Mirage comics - with lots of story and character elements coming from that - and the 2003 cartoon series, which seems to be what her designs for the Turtles are based on.
The story however takes a much darker and tragic turn from the start however. When Master Splinter receives a cursed sword in the mail, everything begins to go wrong very quickly, escalating into a fight that leaves each of the Turtles broken, and missing one of the most important people in their lives - forever.
All of that serves only as a prologue however, with the main story taking place years later, with the Turtles as adults (hence the lack of 'Teenage' in the title). Still broken and driven apart, events begin to conspire to force the brothers back together, not the least of which is Renoir, a new younger mutant turtle who has some complications of his own - like seeming to remember having been a human boy before he was seemingly killed by a wild mutant turtle.
Where will all of this lead? You'll have to read from the beginning to find out, and you can do so from here. Or if you want more direct information about the series from Tigerfog herself, here is the information page.
Page updates for this series are not extremely regular or set to a certain standard, as Tigerfog is often updating prior pages with fixes to be even better than they were before. As such, I can make no promises on how often there will be new pages to review. I'm as eager for more as you are!
To read this story from the very beginning, you can use the archive on the main MNT Gaiden website.