Tory MP Derek Conway has "unreservedly apologised" to MPs after the Commons standards watchdog said he paid his son too much from parliamentary allowances.
Mr Conway paid Freddie to work part time for him as a researcher while he was studying at Newcastle University.
Standards and Privileges Committee MPs said there was "no record" of what work he had done and said the £1,000-plus a month he was paid was too high.
The Old Bexley and Sidcup MP now faces 10 days suspension from the Commons.
The former whip said his son worked about 17 hours a week for him and did not infringe the staffing allowance rules.
He said he "fully" accepted the committee's criticisms and apologised to the Commons, his constituents and his Conservative Association.
He told MPs: "I unreservedly apologise to the House for my administrative shortcomings and the misjudgements I made.
"I have let my family down very badly indeed and no judgement from any quarter could be more harsh than that which I apply to myself."
MPs are given allowances to run their office and pay their staff and there are no rules to stop wives, husbands, sons, daughters and other family members working for them.
But in its critical report, the committee ordered Mr Conway to repay "the overpaid bonus sums" of about £13,000 and pension contributions received by his son.
The committee's MPs found that Freddie Conway was paid at a full-time equivalent rate of £25,970 per year throughout his employment.
However, "no records appear to exist of either actual work that FC did for his father, or of the work he was required to undertake", the MPs said.
"We are astonished that there appears to be no evidence, independent or otherwise, of any aspect of FC's work for his father."
The committee said Freddie Conway, who they refer to as FC, seemed to "have been all but invisible during the period of his employment".
For the majority of that time he was based at Newcastle University where he was engaged in a full time degree course.
'Improper use' of allowances
"He had little or no contact with his father's office, either in the House or in the constituency," the MPs said.
"No record of the work he is supposed to have carried out, or the hours kept. The only evidence available to us of work carried out was that provided by FC and his family."
The MPs said this arrangement was "at the least an improper use of parliamentary allowances" and "at worst, a serious diversion of public funds".
"Our view is that the reality may well be somewhere between the two," they said.
"Taking together our assessments of the salary level paid to FC and the number of hours for which he was remunerated, we are of the view that Mr Conway misused the staffing allowance.
"He should have exercised his judgement more carefully, particularly as a family member was involved, as he could be seen as having a clear personal motivation for paying his son over-generously.
"He also seemed to be oblivious to the broader reputational risks to the House of any perception of personal benefit to his family."
In mitigation, Mr Conway said the parliamentary commissioner for standards had "accepted there was a need for the tasks I had set my son, that he was qualified to undertake them and he did indeed to so".
He said he had paid his son 6% above the mid-point of the lowest pay scales available to MPs for their staff, which was "well below the upper level".
"However, I accept that what is retrospectively considered an 'appropriate sum' was a matter for the committee and I shall comply fully with their requirements," he said.
The committee said there was "conclusive evidence" that Mr Conway authorised bonus payments to his son "that went way beyond the permitted ceiling throughout the period of FC's employment".
"In support of our conclusions, we note that all bonuses for staff authorised by Mr Conway in the previous three years were within the permitted level."
The complaint against Mr Conway was brought by Michael Barnbrook, a retired policeman who stood against him as a candidate for the UK Independence Party, and is now a member of the British National Party.
He told the BBC: "I don't get any personal joy from it. He's my local MP - he's there to work on my behalf. It's my money he's working with and he should be using it properly.
"If he isn't and he's been suspended, or the recommendation is he's suspended, so be it."