How to save modded game data?

Titanium Backup can backup and restore save data

 

Doubt it, you need root to backup and restore data

 

Which data did you try to backup? Android stores app data in multiple places, so it's likely that you didn't pull from the right place.

 

Potentially. Helium promises non rooted app data backup. Never used it myself though.
https://play.google.com/store/apps/details?id=com.koushikdutta.backup

 

So, you did pull data from /data, or just your internal storage?

 

It would be in /data/data. I didn't give the full path since you came off as knowing what you were doing.

 

No, not in your internal storage. The actual path /data. You need a file explorer that can browse the entire file system.

 

It's been a while since I've used Es. Looks like they've changed it up some. Anyway, if it has the option to go directly to a folder, just type in /data and it should take you there. It's a folder on the root of the system, hence the /. You're currently only browsing in somewhere like /storage/emulated, or something similar, which is where user data is typically stored.