Perry Beeches Academy Trust claimed about £2.8m from the Education Funding Agency for free school meals but only kept limited records of its entitlements.
An EFA report said this was a breach of government guidelines.
The trust said it was a genuine administrative error.
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The trust, which runs five schools and looks after 2,400 pupils, has been ordered to hand back £118,000 to the EFA for failing to keep records of pupils entitled to free school meals for the years 2013 and 2014, and only limited data for 2015.
It is the second financial controversy at the trust, which was also found to have paid an additional salary of £160,000 over two years to its chief executive Liam Nolan through a third party agreement - on top of his £120,000-a-year salary.
In a letter to the trust, the EFA has expressed concerns over "significant weaknesses in financial management and governance" of the schools and sought assurances that these concerns will be addressed with adequately qualified staff.
The academy has been asked to update the EFA on its action plan moving forward by 29 April.
A spokesperson for the school said: "This was a genuine administration error on the system as the details were overwritten by someone who mistakenly thought that was the right way to do it.
"The management of administration was one of the points the EFA picked up on in the report and the trust have been working with them to correct procedures such as this one.
"The trust feels that if a mistake has been made and that money has been claimed by the trust in error, then it of course has to be repaid."
A Birmingham academy chain must pay back more than £100,000 in government funding.