How do I properly seal wood rot on a sliding door frame?

First, you really need to determine if the framing beneath the damaged wood is still sound. Grab a screwdriver or a small chisel and gently poke around the cut hole. If the wood is soft, crumbly, or you can easily push the tool through the remaining structure, then a patch won't hold up under stress. If it's just the surface fibers that have failed, a structural repair is posible. If the internal 2x4 is compromised, you're better off replacing the entire vertical piece from top to bottom.

If you decide a patch is feasible, wood epoxy is definitely superior to standard wood filler. Wood filler is meant for cosmetic filling and won't bond with or resist the forces on a structural deck component like a door frame. You want an exterior grade, two-part epoxy that is specifically formulated for wood repair. You should also treat the exposed surfaces with a penetrating wood hardener first to stabilize the material, and then fill the void with the epoxy. After the epoxy cures, it becomes incredibly hard and acts almost like a metal joint. Regarding the sealing, once the epoxy is fully cured, you need a flexible, high-quality exterior sealant. Don't just slap paint on it. Look for something designed for vertical, exposed wood like a polyurethane sealant or even a specific masonry/wood caulk if the joint needs significant movement allowance. This is crucial beacuse the door frame moves seasonally, and a rigid filler or paint will crack and fail again. You have to allow for that expansion. But honestly, because moisture gets trapped in these areas and wood rot progresses from the inside out, I strongly suggest replacing the section rather than attempting a patch. Even if you repair the rot perfectly, if the surrounding wood is already compromised by moisture, it will continue to wicked up and compromise the repair. Fixing the source of the water, like making sure the flashing around the jamb sheds water completely, is a big step, but replacing the damaged piece is the most certain path to a long-term fix.

I agree with the suggestion to replace the whole vertical piece rather than trying to patch the rotted section. Moisture really gets into the framing and those patches rarely last. When I replaced a jamb once, I found that using structural wood screws instead of lag bolts made aligning the new piece much smoother. After cutting out the damaged wood, I always make sure to completely scrape the inner surfaces down to sound material first. That helps prevent hidden rot from migrating into the new repair.

Honestly, even if you get the epoxy perfect, you are going to run into issues with wood breathing. When you seal a door frame up tight, the pressure from the wood expanding and contracting across the seasons builds up somewhere, and eventually, something cracks. I always found that if you were going to patch, you needed to make sure there was some air movement around the joint, not just a plastic barrier. Most of the rot problems start because the moisture just has nowhere to go. You should consider using a traditional wood stain that penetrates rather than just painting over the repair. It lets the wood do its thing.