Billy was headbutted following his side’s defeat to Nottingham Forest in the Championship play off semi-final.
Nottingham Forest season ticket holder Robert Biggs, 30, was jailed for 24 weeks on Thursday after admitting the assault.
But Forest fan Zoe Potts set up the Just Giving page with the aim of raising £500 for a charity of Billy’s choice, following the incident.
Billy chose Boston Spa-based Martin House, which supported him and his partner Jade following the death of their son Luey in 2011.
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Clair Holdsworth, chief executive of Martin House, said: “We would like to offer our heartfelt thanks to Billy and Jade for thinking of Martin House at this time, and hope Billy is recovering from this incident.
“We’d also like to thank Zoe and the hundreds of people who have donated to this fundraiser.
“The money they have raised will make a real difference to children and young people with complex health needs.”
Martin House cares for babies, children and young people with life-limiting conditions from across West, North and East Yorkshire, as well as supporting their families.
Every year it support over 425 children and young people, and their families, plus more than 150 bereaved families at its hospice, in hospitals and in families’ own homes.
The hospice has nine bedrooms in Martin House, and six in Whitby Lodge, which cares for teenagers and young people.
Services include respite stays, symptom control, emergency and community care and end of life care and cost nearly £9million a year.
Bereavement support is offered to families, often for two to three years after their child’s death.
“We also offer bereavement support to families whose child had a life-limiting condition but did not have the opportunity to use the hospice, or following a sudden death,” added a spokesman.