Ten people have been handed on-the-spot fines under the Public Health Act in the Wicklow Mountains today.
Gardaí patrolling the area today say they have told more people to turn around after finding them more than five kilometres from home.
The force got new powers to issue a fixed-charge penalty of up to €100 last Monday.
The fixed charge penalty notice will arrive in the post and a person will have 28 days to pay it.
Up to Thursday, 37 people had been issued the fine.
Under the level five restrictions in place until the end of the month, people are required to stay at home except when travelling for work, education or other essential purposes, with exercise within five kilometres of home allowed.
Garda Headquarters has warned patrols and checkpoints will continue nationwide this weekend to enforce the lockdown rules.
It comes as a local councillor warned that there was 'no doubt' people were travelling from well over 5km away to visit the snowy Wicklow Mountains last weekend.
Shay Cullen - a Fine Gael Councillor in Wicklow - told Newstalk Breakfast that areas seeing a lot of traffic are the Wicklow / Sally gaps, as well as the Glencree and Crone Woods areas of Enniskerry.
A number of cars are also reported to have been towed away over the weekend.
Earlier this week, three people who travelled 80km from Co Meath to Dublin for a burger were also fined for breaching restrictions.
Additional reporting by Stephen Bourke
Main image: Garda patrols in the Wicklow mountains today. Photo: An Garda Síochána via Twitter