So I have rooted my S4 Mini, as described here and installed JellyBean version of Carbon rom for S4 Mini LTE (i9195, my model).
I used this
guide when rooting and I used this
Everything works as should, but my data network is behaveing strangely. It's not that it's not working, it does connect to via H+, 3G (which imediatley turns into DC which is something I haven't seen on stock rom). But it connects only sometimes and doesn't work at other times in places where it definitly should. And 4G never works (in places it worked on stock).
Disregard Wi-fi part, I had some issues with my router, there was never a problem with my phone (at least regarding the Wi-Fi)
My APN is fine, it wouldn't be able to connect otherwise (and I checked the settings).
Ask for any additional information. =)