Last December, the government announced plans to establish a Future Talent Fund to provide £23m of grants to test innovative ways to help disadvantaged pupils with strong academic potential and prevent them falling behind their more affluent peers.
But it has now emerged that the fund will actually be worth £21m and only feature £16m of government funding.
In addition, a fund manager, who will be paid £2m to run the two-year programme, will be expected to raise at least £5m, the Department for Education has confirmed.
A tender document for the fund states: "The fund is expected to support grants worth £21m over its lifetime (2018-20).
"The government will provide £16m of this. The contractor will also be responsible for raising at least £5m additional funding to contribute to the fund; this will supplement DfE funding. The additional funding will come from a variety of alternative sources, but not from state-funded schools."
Announcing further details of the scheme, education minster Nick Gibb said it will fund at least 30 pilot projects between January 2019 and July 2020.
All schools, including those in the independent sector, as well as charities, research organisations and universities will be invited to apply.
Among issues the programme will test is how schools can use their pupil premium funding to support disadvantaged bright pupils.
Other themes covered in the pilots will include curriculum changes, use of digital technology, parental involvement and one to one tuition. Summer schools and after school activities will also be looked at.
"We want to make sure every child reaches their full potential and is not held back because of their circumstances," said Gibb.
"Through this Future Talent Fund we will test new and innovative approaches so that we can find out what works best to ensure the brightest pupils from the most disadvantaged families can excel in their education."
Education Endowment Foundation chief executive Kevan Collins said there is a lack of detailed knowledge about how best to help this group of pupils and welcomed the fund's focus on evaluation.
"At the moment, we know very little about 'what works' for high-attaining disadvantaged pupils. The fund's focus on evaluation will give us much-needed insight into how best to support this group of pupils to reach their full potential," he said.
"Schools need to have the knowledge and the resources of how best to provide stretching lessons for high-attaining pupils, as well as helping low-attainers to make good progress."
Professor Sonia Blandford, chief executive of education charity Achievement for All added: "As an investment in underachievement I welcome the Futures initiative, I would also welcome similar investment in improving outcomes for the more vulnerable."
Analysis of government data by the Education Policy Institute (EPI) published last August found that the attainment gap between the most disadvantaged pupils and their peers had worsened over the past decade.
Those entitled to free school meals for 80 per cent of their time in secondary school are on average more than two years behind their peers in terms of academic achievement, the EPI analysis found.
