About 350 people gathered outside to support them and protest the ban, The Irish Times reported. Many said they will continue to demonstrate against the law.
The Irish law brings the country into line with European Union regulations aimed at protecting wetlands. Peat, decayed vegetation, has long been a source of fuel, but scientists say it accumulates far more slowly than it is cut.
Ireland could face large fines if it fails to enforce the law.
Michael D'Arcy, 43, and Padraic Byrne, 57, both of Killimor, Pat McDonagh, 43, of Portumna, and Tony Parker, 44, of Woodford, appeared in South Loughrea District Court for their first appearance after receiving summonses.
Superintendent Enda Walshe of the National Parks and Wildlife Service said there have been several confrontations with turf-cutters in the 53 bogs designated as areas of special concern.