The figures show looked-after children, pupils in care and those with a child protection plan lag behind their key stage two classmates.
They also show the gap between disadvantaged and non-disadvantaged children in key stage one grew during the coronavirus pandemic.
The Association of School and College Leaders said the most vulnerable pupils have been ‘most heavily affected by the disruption of the pandemic’ and called for greater financial and social support.
The latest Department for Education figures show 19 of 84 children in need in key stage two in Barnsley met the required standard for reading, writing and maths in 2021-22.
For all pupils, this was 59 per cent.
Meanwhile, further DfE figures show the gap between children in need and all pupils in key stage one has grown during the pandemic.
The proportion of children in need across England reaching the expected standard for reading and writing fell by 21 per cent and 28 per cent respectively from 2018/19 to 2021/22.
But attainment for all pupils in the same subjects across the same time period fell by 11 per cent and 17 per cent.
It was a similar story for maths and science, with the percentage of vulnerable pupils meeting the expected grade falling by 20 per cent and 13 per cent respectively compared to 11 per cent and six per cent for all pupils.
The ASCL said vulnerable pupils have been ‘most heavily affected’ by the pandemic.
Margaret Mulholland, SEND and inclusion specialist, said: “As we return to more settled conditions, there must be focused on support for disadvantaged children from early years right through to post-16 education.
“We echo calls for the pupil premium to be weighted more heavily in favour of persistently disadvantaged pupils, and for more research to be done on the drivers of poor outcomes for vulnerable children.
“Greater financial and social support is needed to reduce the effects of deprivation that are having a direct impact on their learning.”
The DfE figures show of the 84 key stage two children in need in Barnsley, 34 reached the expected standard for reading, 21 for writing, and 38 for maths.
For all pupils, 73 per cent met the expected reading standard, 70 per cent in writing and 72 per cent in maths.
A Department for Education spokesperson said: “At the heart of the government’s agenda is an ambition to drive up standards, quality, and outcomes for all pupils.
“Our record speaks for itself with 88 per cent of schools now Ofsted rated good or outstanding, compared to 68 per cent in 2010.( “We know that the pandemic had an impact on pupils learning, which is why we’ve made available almost £5bn in education recovery initiatives, through which nearly three million tutoring courses have started.( “We are also supporting the most disadvantaged and vulnerable pupils through pupil premium funding, which will increase to £2.9bn in 2023/24 - the highest cash terms rate since this funding began.”