Sheffield City Region mayor Dan Jarvis said it "beggared belief" that Mr Sunak's North Yorkshire constituency was put in a higher priority category than Sheffield and Barnsley in the Government's flagship £4.8bn Levelling Up Fund.
And it emerged that Richmondshire was also on a list of 100 areas prioritised for funding for another scheme while the city of Hull, the fourth most deprived local authority area in the country, missed out.
The Chancellor was facing calls to reveal the methodology behind both decisions and was warned he faced a repeat of the Towns Fund 'fiasco' where a number of Tory target seats in the 2019 election were earmarked for up to £25m in regeneration funding despite not meeting government criteria.
Funding packages for the first 45 successful areas, including a number in Yorkshire, were revealed this week and 40 were in areas which now have Conservative MPs.
Labour leader Sir Keir Starmer claimed the allocation of £1 billion funding to mainly Conservative seats will look "fishy" to the public but Prime Minister Boris Johnson said it was partly due to his success in the general election meaning that the Tories now represented a lot of towns.
The Levelling Up Fund, first announced last year, will see £4.8bn handed out over four years for "impactful infrastructure projects" in areas where it will make the biggest difference.
A report released this week revealed that all local areas have been placed in one of three categories, with the top category "representing the highest level of identified need". Preference will be given to bids from higher priority areas.
It added: "The metrics used to determine a given place’s category includes consideration of its need for economic recovery, regeneration and improved connectivity."
In a letter to the Chancellor published yesterday, Mr Jarvis wrote that Richmondshire was in a higher category of need than areas like Barnsley, Sheffield, Salford and Halton which have much higher rates of Covid-19 deaths.
He wrote: "Whatever the exact formula, the practical reality is that you have allocated support in a way that favours places that are affluent over those that are deprived; places that are resilient over those that are vulnerable; places that have suffered less from COVID over those that have suffered more.
"Poorer communities across the North have been treated especially unfairly, making a mockery of the government’s commitment to levelling up. This is part of a wider pattern. The pandemic has disproportionately targeted the most disadvantaged communities: government support has not."
A senior councillor in Richmondshire said the rural district had problems of its own and was in need of government support because of a lack of public transport and good jobs.
And asked about the formula on Wednesday, Mr Sunak said it was “based on an index of economic need, which is transparently published” and “a bunch of objective measures”.
Local authorities will bid for the funding and the number of bids they can make will depend on how many MPs are in their area. MPs are invited to be involved in lobbying for funding but can only back one bid they see as a priority.
Treasury officials point out that as well as Richmondshire in the top category, areas such as Blackburn, Blackpool, Chesterfield, Gosport, Liverpool, Middleborough, Oldham, Redcar and Cleveland have been included.
Keith Aspden, the Liberal Democrat leader of York council, which is in the lowest category for the Levelling Up Fund, said: "Questions remain to be answered about how strategic, and how fair, the current investment plan is.
"Fairness and transparency must be imbedded in the Government’s regeneration funding schemes for the region to succeed and drive recovery together, rather than see the North put on course for a divided recovery."
It comes after a Budget where Mr Sunak extended the job-saving furlough scheme until September as well as cuts to VAT and business rates to aid the tourism and hospitality sectors.
A northern campus of the Treasury will be moved to Darlington and Leeds will get the UK's first infrastructure bank, while the Humber and Teesside will both get new 'freeport' status.
But James Muir, Chair of the Sheffield City Region Local Enterprise Partnership, said: “Our economy is still in crisis mode and so the extension of support for businesses must be welcomed but it does not go far enough.
"Indeed, many of the Chancellor’s initiatives are things we told him we needed in South Yorkshire last summer. But it’s hard to see what’s in the Budget that will support the longer-term project to level up our region."
A Treasury spokesman said: “All local areas in the UK will be able to apply for funding through the levelling up fund.
“The bandings do not represent eligibility criteria – and money will be allocated to the areas most in need.
“Further technical details will be published by the Government in due course.”