The list has been released by the Independent Parliamentary Standards Authority (IPSA) and includes ministers Tobias Ellwood and Edward Timpson.
A total of £2,105.43 was written off last year, and IPSA insists they contacted the individuals concerned asking for the cash several times.
The full list of 26 MPs named by IPSA:
But a number of MPs dispute the claims, with some saying they know nothing about them.
Stephen Williams, who was Lib Dem MP for Bristol West from 2005-2015, told Sky's Darren McCaffrey it was "news to him" that he owed money.
"All clear with them," he tweeted McCaffrey.
"They may have allocated something to wrong heading, a very common error. I don't owe anything."
The debts written off range from a few pounds to hundreds.
The majority of the spending was on official credit cards, which are paid off automatically by IPSA before it is checked whether the expenditure is allowed.
Mr Timpson, who is children's minister, put a £127.50 "public transport" bill on his card, and later ticked a box on a form to indicate he did not want to claim back the amount.
He has not repaid the money, according to IPSA.
Mr Ellwood, a Foreign Office minister, was listed as owing money for three claims.
Spending of £5 on food and drink was deemed to be outside of the rules, while a £17 train ticket was a duplicate.
Mr Ellwood, who wrote a letter to IPSA backing a 10% pay rise for MPs, also said he did not want to claim for a £4.50 parking charge.
Chris Skidmore, a parliamentary aide to Chancellor George Osborne, spent £125 on a hotel in London, but this was deemed outside the rules.
Equalities minister Caroline Dinenage paid a £13.50 constituency office telephone bill on a credit card, but this was later ruled to be ineligble.
Jonathan Isaby, chief executive of the TaxPayers' Alliance, said: "If sitting MPs are unwilling to pay what is due, the simple solution would be for the amount to be docked from their next salary payment.
"Those former MPs who have been named and shamed should also do the honourable thing and pay up - and if they are unwilling to do so, then surely the obvious sanction would be to remove the parliamentary pass they enjoy as a former member until such time as their debts to the taxpayer are paid up."
Each MP's expenses and office costs for 2014-15 have also been published, with spending rising by 1.6% to nearly £106m.
Spending on flats, hotels, travel and subsistence was down around £150,000 to £11.6m.
Staffing costs and numbers have increased. MPs now employ more than 4,000 members of staff - an increase of more than a third on six years ago.
Last year staffing costs went up by £2.2m to £82.7m.