I want to start a sitter or companion business in Georgia

Sure you might... but are you qualified to? They aren't illegal.

Can I start a siter buiness in Georgia as an a first time offender who is on probation

What was the offense?

**edited**

Most likely, no you can't as this business, and yourself, would need to be licensed, bonded, and insured. You would also need some medical background and/or training.