Captain reported a near miss with another aircraft while on an initial approach and communicating with ATC. The PF responded to a TCAS RA and maneuvered to avoid the other aircraft; then landed safely.

Narrative

Inbound 3000 ft. 10 nm ESE of PDK Atlanta approach asked if we had the field insight which we did. Cleared for the visual 3R Switch to Tower...seeing a target on TCAS 4 nm ahead constant bearing decreasing range indicating -300 feet; I asked if approach was talking to them. ATC stated negative do you want to stay with me? I stated we will maintain 3000 and stay with ATC until we passed over traffic; since we were being sequenced into PDK with multiple targets all around. At 5.4 nm from PDK just about to cross over traffic; the light civil must have noticed us on his gadget; maybe; maybe not; but as if Murphy was his copilot he initiated a climb towards us. PF took evasive action with TARA alert and climbed. TCAS altitude indicated -100 as at closest point of traffic below us. When clear of conflict we notified ATC we responded to RA and are clear; switching to tower and descending for visual. Landed uneventful.Suggestions: Although legal to pass outside of very congested airport without comms with ATC because Below the Bravo"; not a good idea when the airport you are passing by lands jets."