Can I marry my fiance' in jasper county jail jasper, Texas

Normally you don't.

But if you want to try, you have to speak to the chief deputy over the jail and get his permission, Then arrangements will have to be made (if you don't already have license) to get a marriage license, this may require special costs to be paid to the jail for the officers times to do this.

Since jail is for detaining between arrest and court, and or for up to one year punishment, normally since it is for such a short time, things like marriage is not allowed, as it may be in a state prison.

Start here,

Jasper County | Marriage License