The driver of the car was stopped at 4.50am on Monday 15 March on the A64 near Bilbrough.
All four were given fixed penalty notices by North Yorkshire Police for being outside their place of residence.
It comes as police revealed more breaches of stay at home regulations, including five men who were given fines for holding a hot tub party in a lodge near York.
Scarborough once again saw the highest number of fines issued, with 50 given out across the area, including 20 for two house parties that took place over the weekend.
Hambleton saw 15 fines issued and Harrogate had 12.
Craven and Richmond had the lowest number of fixed penalty notices with three and two respectively.
Some 1,662 fines have been issued across York and North Yorkshire in this period of lockdown with 3,555 issued since the beginning of restrictions almost a year ago.
Police have said they will increase their presence in the county as lockdown restrictions begin to lift and around Easter.
Supt Mike Walker said: "We can all see that better times are on the horizon, that’s why we must keep going and not allow all the hard work and sacrifice to be undone through complacency.
"We all must keep adhering to the health protection regulations around travel and gatherings, maintaining social distance, wearing face coverings in shops and on public transport, and keeping our hands as clean as possible.
"From a policing point of view, we will continue to play our part in tackling the public health crisis as we head towards the Easter holidays.
"When it is safe to do so, we will welcome visitors to the county again. However, everyone can expect to see an increased policing presence as we work alongside our partners to help keep the virus at bay in the weeks and months ahead."