At the earthquake-shattered remains of the Jem Mala-Dim Moslem mosque on the outskirts of this modern Soviet Central Asian city, all that could be heard one morning recently was the moaning wind from the depths of the Kara-Kum desert and the intermittent wail of a diseased Turkmeni infant, brought to the ancient holy place by parents seeking a miracle to save lhis life.

While his father, a weathered Turkmeni from a Soviet state farm 30 miles to the east, waited in the shade of a broken wall, his grandmother, mother and two other healthy children carried this swaddled sick boy through the mosque ruins, praying from time to time before certain stones and once crawling three times through a sand-choked archway.

A mighty Moslem citadel since the 16th Century, the mosque was destroyed in the 1948 earthquake that leveled all of Ashkhabad except for three buildings and the marble statue of Lenin in the city square.

Ashkhabad was rebuilt; the mosque was not. But it still functions today as a powerful magnet to Moslem believers. The desolate site at the edge of the desert is criss-crossed with paths well-beaten by Moslems who come there to venerate their dead, seek miraculous cures for infertility, and somehow reverse the sentences sometimes pronounced in their loved ones by modern doctors.

This was the case with the farmer, who said physicikans had given uphope for his afflicted three-month old son. Although he could neither read nor comprehend the Arabic in his family's hand-me-down Koran, he said, he was a moslem believer.

Despite almost 60 years of antireligious propaganda, such folk practices endure throughout Soviet Central Asia. This stubborn reserve of belief continues to challenge and dismay the authorities, who denounce these and similar ancient practices as "contradictory to the Soviet way of life."

The Communist chief of Urkmenia at the 1976 party plenum charged that with local party officials' "connivance, a large number of unofficial ministers of religion lead a parasitic existence, propagate reactionary ideas and divert believers from conscientious, socially useful labor."

M. G. Gapurov, the party chief, called for "a stepped-up struggle against religious psychology and especially against the Moslem cult." He explained that "Islam, like any religion, often plays the role of 'custodian' of reactionary national customs and traditions and aroused feelings of national exclusiveness."

He called for a stamping out of traditional exclusiveness."

He and other Soviet leaders have also sought to eradicate kalym , or bride price, a traditional Central Asian custom in which a suitor may be required to pay up to $10,000 rubles (about $14,000 at the official exchange rate) in order to marry the girl of his choice. If he does not complete payment in time and the wedding goes ahead, the bride's family sometimes kidnaps her in the custom known as kaitarma .

Both practices have been made criminal offenses in Turkmenia, but they persist.

Other persistent folkways that distress party officials are shamanism and belief in miraculous cures. One historian writing in the journal Science and Religion declared that "the custom of making pilgrimages to the burial places of saints for the purpose of curing women's infertility... is probably the most characteristic religious phenomenon in Central Asia today."

The historian, G. Snesarev, wrote that "childless women persist in observing many magical and sacrificial rituals that actually are pre-Moslem in origin." These include visits to ancient burial tombs, animal sacrifice or making" miniature models of cradles and babies, such as those found by Western visitors the Jem Mala-Dim Mosque.