There are a few different ones and there's almost always something going on each night.
IRS is a league that I'm a series organizer for, but @aceboy127
set it up and added leaders as he went along. We have a nice group now coming up with great racing series ideas and we put them out for a season at a time. Currently we run a series with the 86 GRMN and Gr. 4 cars, while also a "Trans Am" style series with multiple classes. They run Mondays and Saturdays respectively. IRS uses the concepts of real world racing to recreate or replicate them in a GTSport environment. At the moment we are finalizing an IMSA series using their line up of GT cars but with Gr. 3 and Gr. 4 on track together. Come check us out at the main hub thread for some general info, and the links to the series that are currently running are in my signature below. We'd love to have you!
SNAIL started as a dedicated one-make spec series but has grown to host other series throughout the week with other formats. Sunday night is their spec night, with Tuesdays being an Endurance League and Thursdays their mock rehearsal practice night that follows the same format as Sunday. They are also starting a Super Formula series on Wednesdays.
ARL is a new league that likes to use tire and fuel wear settings similar to the FIA races which gets a nice cross pollination with those drivers looking for FIA style races. Saturday nights they run Gr. 3 with all the cars available, with two allotments per car to create variety. On Wednesdays they have a Gr. 4 series that is one-make and each season the car changes.
Everything I have mentioned so far runs in the evenings, generally from 8pm EST to about 1am. ARL starts a little later because their leaders are in Central Time, one hour before EST. @TexasJDC
has links to his series in his signature as well. For SNAIL, you can type in snailracing.org and it will redirect you to the their main thread which discusses everything but is also the focus for the Sunday night races. They have a dedicated sub-forum now due to the high volume of activity there. Between everything listed I'm sure you'll find something you like and we hope to see you on track soon!
(I need to save this post for copy/pasting in future interest threads)