In Scotland alone, it means the UK Government will spend more than £100 million on projects usually managed by the Scottish Parliament.
The new “Shared Prosperity Fund” is designed to replace European Commission development grants, which the UK lost access to when it left the EU.
The Scottish Government has also published plans on how it will replace EU funds.
Mr Barclay also accused the Scottish Government of deliberately ignoring the financial support it has received amid demands for more money to be released.
Scottish Finance Secretary Kate Forbes publicly called for the UK Government to release £21.3 billion of its financial reserves, an estimated £1.7 billion of which would come to Scotland.
But Mr Barclay, the minister responsible for public spending, has said the Scottish Government “continue to wilfully ignore the huge amount of support” already provided.
In a letter to Ms Forbes, Mr Barclay lists various coronavirus support, including the furlough scheme, the Treasury has made available, in addition to £8.6 billion of additional guaranteed funding this year.
Mr Barclay said: “Together these schemes have supported more than 930,000 jobs in Scotland and will continue to support Scottish jobs throughout the winter.
“They continue to be provided with incredible speed, thanks to the ingenuity and expertise of HMRC.”
He stated that the total funding for Scotland through the Barnett funding formula for the next financial year was more than £38 billion.
“This equates to around £129 per head for every £100 per head the UK Government spends in England on matters devolved in Scotland,” he said.
“We will take decisions on spending from the UK reserve during 2021-22, just as you will with your own reserve, but the scale of the UK reserve reflects the likely costs associated with continued testing and vaccine procurement which the UK Government is funding UK-wide.
“It is therefore important that we use the UK reserve for funding pressures as they arise.”
In her letter to Rishi Sunak earlier this week, Ms Forbes argued it was “imperative” he immediately release the cash set aside to deal with Covid-19 in the next financial year.
She told the Conservative Chancellor: “The new strain of Covid and subsequent tightening of restrictions mean that further funding is required now to provide certainty to the end of this financial year and into 2021-22.”
Mr Sunak held some £21.3 billion in reserve to help with the UK’s coronavirus efforts when he announced his spending review in December.
Ministers in Edinburgh have already received an additional £8.6 billion from the UK Government to help mitigate the impact of Covid-19.
The Holyrood Finance Secretary made the plea for the additional cash to be released just over two weeks before she is due to announce the Scottish Government’s draft Budget for 2021-22 to MSPs on January 28.
Speaking as the letter was sent, Ms Forbes said: “We welcome the £8.6 billion received so far in Covid-19 consequentials. Virtually all of this has already been allocated and is being spent supporting our businesses, NHS, public services and the rollout of vaccines.
“However, demand continues to outstrip the resources available and our inability to borrow on the financial markets, or even use unspent capital funding to address immediate needs, leaves us reliant on the UK Government.
“The new strain of the virus and subsequent tightening of restrictions mean that further funding is required now. I urge the UK Government to release our share of these reserves so we can provide the maximum support to businesses and the health service during this critical period.”