The 12-year-old was struck by a car on Brett Street in Bridlington and died of his injuries the following morning.
It is the third tragedy to hit Taylor's mum Katie in just over a decade. Taylor's father Stuart Swift died in a road accident at Carnaby 11 years ago.
Last year, her husband Andy Tolley, Taylor's stepfather was killed in a motorcycle accident at Bempton.
An online fund set up to support the family has seen more than £6,000 pledged by the Bridlington community in the first 36 hours.
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Family friend Sherri Miller, who started the web page, said: "I am raising money for Katie to be able to lay her son to rest without the stress of money, all contributions will be much appreciated."
Around 450 people have donated so far. A similar campaign set up following Andy's death last September raised £2,746 for the family.
A tribute to Taylor, who was a pupil at Bridlington School, is being planned for Wednesday afternoon. Friends and family are planning to release balloons in his memory from the fields near to his home in Gypsey Road at 4pm.
Organiser Julie Deighton said: "We are hoping to see lots of people there to pay their respects to this beautiful little boy who was loved so much by everyone that knew him."