Sometimes it is difficult to pin down original dates. It is claimed that Royal Enfield introduced a motorized quadricycle and a tricycle in 1898. This may or may not be true. According to this article about the Stanley Show (presumably of 1898) published in the Coventry Herald of February 24th 1899, there indeed was a tricycle in the show. No mention of a quad. Notice the (now quaint) final remark about cars.
However, the Morning Post of London November 18t 1899 does mention quads in their article about that year's Stanley Show,
Finally, in The Autocar magazine it mentions tricycles and quads and also Enfield cars for the Stanley Show of 1900.