Dog the Bounty Hunter -- In Dogfight Over Fugitive's Arrest

Dog the Bounty Hunter is so into dogs, he allegedly tried to buy one off a fugitive ... while his cohorts were kicking in the guy's front door to haul his ass off to jail ... but Dog's lawyer says the fugitive is lying about him wanting to buying the pooch.

Dog's latest catch, James Hawkins tells TMZ ... he was arrested earlier this month at his Texas home, and as he was cuffed he claims Dog immediately locked eyes with his great dane -- and whipped out $1,000 cash to take it away.

Hawkins was pissed, and told Dog to lay off Duke -- a 7-year-old, 200 lb. pooch. He says Duke doesn't need to be rescued by DBH or anyone else.

Dog's lawyer, Marty Singer, tells TMZ his client NEVER tried to buy Duke ... never offered him a cent for the animal.

Hawkins -- who was wanted for failing to pay bond on a previous arrest -- is considering suing Dog for trespassing ... and forcing him to sign release papers for the reality show.

Meanwhile, Hawkins' fam didn't seem offended -- they all posed for pics with Beth Chapman while Dog was busting dear ole dad.