The village lies in a gently undulating landscape at the southern tip of the Mohelnice furrow along a stream of an unnamed name flowing from the left side into the Morava River.
The place where the village is now located, the fertile floodplain of the Morava River, has been inhabited since prehistoric times due to its location. On the right bank of the Morava River, according to archaeological research, was a large settlement already in the early Stone Age (2000 BC). Furthermore, a burial ground from the Bronze Age of Lusatian culture (approximately 1300-500 BC) and many bronze objects were found.
The name of the village recalls that in the Middle Ages the village was surrounded by the Morava River, which spilled into wetlands, which provided excellent conditions for reed growth, old Czech cherry. The first mention in written sources dates from 1353 when there was a property of a certain Mrs. Bolka of Otaslavice. Individual parts of Třeština were held by many different owners from the ranks of small nobility until the 15th century, when it became part of the Zábřeh estate. Land registers have been kept since 1609. In the 17th century, the estate passed into the hands of Ladislav Velen of Žerotín. He was one of the Moravian leaders of the uprising of the Estates and after his defeat on White Mountain he had to flee abroad. His extensive estate was acquired during the confiscation of Prince Charles of Liechtenstein and the property of the Liechtenstein family remained Třeština until 1848. During the Seven Years War, the village was plundered by Prussian soldiers and in addition, in 1754 and 1774, it was hit by large fires. The first mention of the school dates back to 1820, it was taught on the site of a municipal forge and the first teacher was Mr. František Šula. František Poštulka, an important local history writer of North Moravia, was also born in Třeština.
At the end of the 19th century, Třeština quickly became one of the leading Czech agricultural villages in the Mohelnice region. In 1834, 319 people lived in 45 houses.
At the turn of the century, Třeština markedly entered Czech history of technology. In the 1890s Hubert Plhák, the mill owner in Háj, decided to set up a power plant that would supply energy to the mill machines. He bought two dynamos, which he put into operation, but in 1898 the mill burnt down and fire destroyed the dynamos and mill machines. His money was enough for the new construction of the mill, and could not bury new power equipment. However, since he had already shown the benefits of his electricity, he and his friends persuaded the management of the local dairy cooperative to participate in the implementation of Plhak's plans. In 1901, the first Moravian agricultural power plant was established in Háj, the first in the Austro-Hungarian monarchy, which electrified the surrounding village by overhead lines. Třeština outperformed not only Prague but Vienna.
The work of Hubert Plhák was followed by his son Karel, who had a new, independent hydroelectric power plant built in Háj in 1922. The buildings were designed by Jan Kotěra, talented pupils of the architect Jan Kotěra, who built one of the gems of modern architecture.
Attempts to establish a collective farm in Třeština in 1950 and 1952 always resulted in the collapse of the cooperative, only in 1955 was a viable unit, which in 1975 merged with the agricultural cooperative Úsovsko based in klopina. The dairy was abolished during the Second World War and its building was eventually used for municipal self-government and trade.