Nearly no connection. One ancient writer tried to draw a link, but he was wrong.

The Dardania of Trojan myth, near Mt Ida, was probably never real; no ancient geographer ever managed to find out anything about it beyond what it says in Iliad 20, that is was on the slope of Mt Ida.

The classical-era city of Dardania was named after the mythical one, but it wasn't anywhere near Mt Ida, it was on the Hellespont. It wasn't an especially important settlement.

The Dardani of Moesia, by contrast, were very much a real people, who are reported in that region -- southwestern Moesia, in or near modern Kosovo -- from the Macedonian conquest, on to their fight for independence, to their annexation by the Romans, to their status as a Roman province in the 3rd century CE.

There were several Dardanuses in antiquity besides the mythical Trojan one, so there's no particular reason to go drawing links, other than a similar-sounding name. Names have a finite number of syllables to be made out of, and inevitably there's going to be some chance resemblances.

Still, the resemblance drew one ancient writer to try and link them with the mythical Dardanians. Solinus 2.51 (writing in the 3rd century CE):

The route out of Italy passes through the Liburnians, who are an Asian race; to the foot of Dalmatia, that is, Dalmatia on the Illyrian limes. In the corner of that is where the Dardanians have their territory: they are people of Trojan stock, who have gone wild and have barbarian customs.

The last bit, 'gone wild' and 'barbarian customs', is a motif drawn from stereotypes in the Roman world: the details that appear in Strabo 7.5.7 -- the Moesian Dardanians live in caves that they dig under dunghills, but they're very fond of music -- are lurid, and have no real-world implications for the historical Dardanians. I wouldn't put any stock in those details, nor in Solinus' attribution of Trojan ancestry.