In July, Conor McGinn, who is from south Armagh, claimed the Labour leader suggested phoning his father.
It followed an interview in which he called for Mr Corbyn to "reach out beyond his comfort zone".
A spokesman for Mr Corbyn said at the time that it was "untrue".
The St Helens MP told BBC Radio Four's Westminster Hour: "The modus operandi that he (Mr Corbyn) and the people around him were trying to do, involving my family, was to isolate and ostracise me from them and from the community I am very proud to come from -  which is an Irish, nationalist community in south Armagh."
The MP claimed that after he spoke out about Mr Corbyn in May, he got a call from the Labour whips' office saying the party leader had initially asked for his resignation and then considered sacking him.
But subsequently, through his spokesman, he had asked for an apology and retraction, which Mr McGinn refused to make.
The MP said he then texted the Labour leader to make clear no offence was intended and reiterate that their friendship was important to him and asking for a meeting.
He received no response, but said he was then informed by the whips' office that Mr Corbyn had proposed asking the MP's father, Pat, to intervene.
Pat McGinn was Sinn Féin councillor in Newry for many years, serving as the council's mayor between 2005 and 2006.
A Labour MP who accused Jeremy Corbyn of threatening to use his father - former Sinn Féin mayor Pat McGinn - to "bully me into submission" has spoken publicly about the row.