I have a 12" overhang on a Gable end and I have a big tree growing right by the roof line. I need to cut in to the overhang 4" to 6" to give the tree some room. I don't want to cut the tree down. It's about 3' through. I know I'm going to have to cut the outer rafter and drip edge. How can I support this with out alot of work? The trunk of the tree is growing right in the center of on one side of the Gable. It's a 12" overhang and all finished.

What is your soffit material? Basically, I guess the approach would be to cut into the overhang with a Sawzall, and insert pieces of lumber to close the ends of the cut. I would cut the shingles, with a utility knife, so they will overhang the new cuts by an inch on each of the three sides, so that you can install 3/4-inch finish pieces to match your existing fascia, and the roofing will then overlap the finish pieces. Glue all the cut shingles to the sheathing with roofing cement.

The soffit is made of plywood. How can I brace the overhang so it wouldn't sag? Or does it need it? Because I'm going to be cutting the outer rafter.

It all depends how the fly rafter is framed and attached, and you won't know that until you cut, unless the framing is visible in the attic. If you're lucky, it will be framed with supports at least every 48 inches, the proper method despite what was posted in another thread, and if you're really lucky, it will be supported by outriggers of 2x4's let into the tops of a few main rafters, which is the best way to frame a fly rafter. The worst case is that the fly rafter spans all the way from ridge to rough fascia, and if that's the case, yes, it will sag a little, but will be held by the sheathing and soffit. In that case, you will have to either support the rafter temporarily with a 2x4 bracket back to the side of the house above and below the cut, before you cut, or shove it back into place after you cut, as you insert the blocks.

What you should be cutting is the tree. Tree roots do a lot of damage to homes. I suggest that you remove the tree rather then modify the house. The branch structure is basicly the outline of the roots below. the farther the branches go out from the center the farther the roots. If the foundation is preventing the tree from growing the roots on one side you have an unstable tree. Add water and wind and you have a house with a foundation failure when it blows over.

Thanks Richard for that information. Is the Fly rafter usually a 2x4 or 2x6? So do you think ladder blocking on each side of the tree will support it? I was thinking about using joist hanger for the ladder blocking that fasten to the house instead of toe nailing it. What do you think? Also what would be better nailing or screwing the framing together? I appreciate all your help.

The fly rafter should be the same as the other rafters, but it's possible a smaller size was used if it was properly supported. It's not likely to be smaller than a 2x6. I think a joist hanger would be overkill. Screws aren't a bad idea, and toenailing is fine, too, because the loads are small.

I'm with The Home Care Club 100%.
If the trees that close to the home at some point the limbs going to move enough to hit the edge of the roof and do damage. Having shade that close to the house is going to cause more fungus to grown on that side of the house. shortening the over hang is going to allow more more water to run down the side of the house.
What are you going to do as the limb keeps growing?