BBC Wales political reporter
Ieuan Wyn Jones has hailed the service a huge success
The Conservatives said a subsidised north-south air link in Wales should be renamed 'Ieuan air' because the deputy first minister is "chief beneficiary".
Plaid Cymru leader Ieuan Wyn Jones told Conservatives he had used the service 42 times since its launch a year ago.
Plaid said it was "no surprise" the only north Wales cabinet member used it more and it was a "tiny proportion" of 14,000 journeys taken on the service.
The Anglesey-Cardiff flight's subsidy is Ł2.4m over three years.
Mr Jones is AM for Anglesey, as well as economy and transport minister.
Mr Jones celebrated the first anniversary of the service last Friday by joining a special flight on the 18-seater aircraft.
He said that the service, operated by Highland Airways, was a "huge success", beating expectations.
The airline said it had been "astonished" at the uptake.
Deputy First Minister Ieuan Wyn Jones - 42 journeys
Education Minister Jane Hutt - six journeys
Rural Affairs Minister Elin Jones - three
Heritage Minister Rhodri Glyn Thomas - two
First Minister Rhodri Morgan, Finance Minister Andrew Davies, Social Justice Minister Brian Gibbons - one journey each
Sustainability Minister Jane Davidson and Health Minister Edwina Hart - no journeys
Numbers of flights between Anglesey and Cardiff, up to 16 April 2008. Source: Welsh Conservative Party
The assembly government helps finance two daily return flights, Monday to Friday, between Valley in Anglesey and Cardiff International Airport in the Vale of Glamorgan.
In a letter to Welsh Conservative leader Nick Bourne, Mr Jones said he had used the service 42 times, and staff in his private office eight times.
Mr Jones said staff in his assembly government department had taken the flights on 68 occasions.
The Conservatives said figures obtained by the party showed his ministerial colleagues had only used the service "on a handful of occasions".
Ministerial officials have also used the service.
'Benefit the many'
Shadow Transport Minister Andrew Davies said the flights were "clearly not the answer" to improving transport links between north and south Wales.
"The main beneficiary from its introduction seems to be the deputy first minister, who just so happens to be the local assembly member," he said.
"He's used the service so often there is a strong case for re-naming it 'Ieuan Air'.
"Most people in north Wales get no benefit whatsoever from this service," Mr Davies added.
"We have long-argued that ministers would be far better channelling funding into improving public transport to benefit the many, not the few."
He argued money would be better spent on improving train services, road and public transport in general.
Plaid Cymru responded robustly to the Conservative' claims, accusing the opposition party of making "cheap points" and calling for it to show "consistency" and "commitment" to developing the north west Wales economy.
A statement continued: "As the only cabinet minister who lives in north Wales it should be no surprise to anybody that Ieuan Wyn Jones uses the north-south air link more than any of the south Wales based ministers.
Mr Jones's use of the service was only a "tiny proportion" of the 14,133 journeys taken on this service in its first year.
"The Conservative assembly leader would of course scrap the air link depriving businesses and families of a crucial service," said the spokesman.
"Which other confident, modern European nation doesn't have swift, reliable inter-regional links?"
Plaid said both Conservative economic spokesperson Dylan Jones Evans and Tory parliamentary candidate for Ynys Mon Trefor Jones had called for the service to be established.
The spokesman added that Clwyd West AM Darren Millar had wanted to move the service from Anglesey to Liverpool "to make it more convenient for him and his constituents".