I have a roof over my deck. The posts that support the roof are attached to the deck via simpson timber screws (as seen in the photo below). Is there a better method or bracket I could utilize to beef up this connection?
Use of long carriage headed bolts fitted into holes that are bored all the way through the post and also through the deck joist underneath will be a stronger connection. If bolts of 1/2" diameter are used (2 or 3 bolts depending upon the width of the deck joist) with flat washers and hex nuts they can be tightened a lot and be stronger than those two screws.
One thing to consider is if the deck joist itself is sturdy enough. We cannot see it in your picture but the tall post can act as a very long lever arm and the deck joist could easily be twisted. One way help to reduce the movement of the post side to side is to add additional angle braces from above down to the posts.