The pair is said to have engaged in fisticuffs during a workshop for Regional executives and Parliamentary Candidates at the Kingston Hotel in Takoradi.
News of the fight first broke on Monday, however, there was no official communication from the New Patriotic Party (NPP).
However, it appears the fight indeed happened, with trending photos showing Mr. Bissue with a bruised face.
One of the photos also shows the presidential staffer with a bloodied eye, which was being examined.
Joy News reports that Mr. Bissue and the Tarkwa-Nsuem MP have not been seeing eye-to-eye for some time now.
The report claims the bad blood between the pair started when Mr. Bissue decided to support an independent candidate during the parliamentary primaries, instead of the incumbent.
The report further cites an eyewitness account, which claims Mr. Bissue grabbed the hands of Mr. Duker and bit it several times during the fight.
The MP is said to have bled profusely from the bite, leading to the pair exchanging blows.