Wiktionary
jog on
interj. (context idiomatic dismissal English) go away vb. (context idiomatic English) To continue with one's pursuit
Usage examples of "jog on".
The next day, September yth, she left for an early morning jog on the boardwalk.
I was sneaking in a late-afternoon jog on the bike path at the beach when I'd spotted them sauntering along ahead of me.
So Calvin turned his attention to keeping the air in front of his face clear of ash, as he began to jog on in the direction that he had last seen Arthur Stuart's group going.
He would very patiently jog on the same spot in front of me, or he would take off in a short run and return to where I was, so I could see how he moved.