Try checking with the R&D Vendors in WT/HoD, as well as on the Brokers. I "think" Beta Mods drop in the t1 Challenges as well.
Your gear has different colored sockets which indicate the color mods you should place in them. Before you can make a Beta Mod you need to get the plan (from an instance/mission or from the broker), there are many different plans with different levels (currently the highest level is V Expert). Once you have gotten a plan you can research it by double clicking it if you play on the pc or hitting X twice on the ps3. Once you have researched the plan, you will need to collect exoBITS to make exoBYTES, It takes 8 exoBITS to make 1 exoBYTE. You can turn exoBITS into exoBYTES at the R&D station which can be found in numerous locations in the WATCH TOWER (Tech wing, Magic wing, and Meta wing). R&D stations are also located in some Police stations and they look like this. Once you have reach the R&D station you will see NPC's near it, you will need to buy a BETA interface from one of them then return to the R&D station, turn your exobits into exobytes then scroll down the list of researched plans you have and choose which BETA mod you want to make. If you are a little confused this video can give you an even better understanding.
