The 12-year-old girl was issued with a community resolution for early intervention action for using a motor vehicle on a road without a licence or insurance.
She was also issued with a Section 59 notice which means the vehicle can be seized if it is used illegally, or in an anti-social manner, again.
During the operation, officers also issued four Traffic Offence Reports (TORs) for speeding in Walton ward.
A further TOR was issued for no MOT in Sitlington ward and one TOR was issued for no MOT in Ryhill ward.
PC Richard Shaw, of Castleford NPT, who was involved in the operation, said: "This operation was carried out to help address community concerns about speeding and the use of scooters and off-road bikes on roads in the district.
"We stopped a child who was riding a quad bike on the main road through South Kirkby. Use of off-road vehicles in this way puts both the rider and other road users at risk.
"We will continue to act on information from members of the public and I would urge people to report any anti-social or illegal use of off-road vehicles to us."
Anyone reporting nuisance off-road vehicles can call 101 or use the dedicated form on the West Yorkshire Police website.
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