Our “Shady” grass seed blend is just what you need since it can grow without any direct sun at all. However, since you mention moss, that would indicate that the soil in that area is too acidic for grass to survive.  You’ll need to correct that.  It isn’t difficult.  You’ll just need to do a soil pH test and apply the amount of limestone it indicates to bring the soil to a pH of 7.0.  Here’s a link that will walk you through the process:

https://blog.timesunion.com/gardening/starting-a-lawn-from-seed-better-get-to-it/7338/