In the 1890s, coins for 1⁄12 and ¼ anna (⅓ and 1 paisa) were minted specifically for use in Muscat and Oman by ruler Faisal bin Turki. Before 1940, the Indian rupee and the Maria Theresa Thaler (known locally as the Rial) were the main currencies circulating in Muscat and Oman, as the state was then known, with rupees circulating on the coast and Thaler in the interior. Maria Theresa Thaler were valued at 230 paisa, with 64 paisa equal to the rupee. In AH 1359 (1940), coins were introduced for use in Dhofar region in denominations of 10, 20 and 50 baisa. ½ Rial coins were added in AH 1367 (1948), followed by 3 baisa in AH 1378 (1959) for Dhofar region as well. In AH 1365 (1946), 2, 5 and 20 baisa (mistakenly written as baiza) coins were introduced for general use in Oman. In AH 1378 (1959) Rial Saidi (not to be confused with Saudi riyal) and later in AH 1380 (1960) and AH 1381 (1961) ½  Rial Saidi were introduced in Oman. Saidi Riyal was equal to the British pound. It replaced the Gulf rupee at a rate of approximately 21 rupees to the Saidi Rial.

In AH 1380 (1960) 3 baisa and in AH 1381 (1961) 5 baisa were particularly introduced for Muscat province. The Indian Rupee and, from 1959, the Gulf Rupee continued to circulate in Oman till 1970. The Kuwaiti Dinar from 1961 and Bahraini Dinar from 1965 were also concurrently used till 1970. The new Saidi Rial was subdivided into 1000 baisa. The Rial Omani replaced the Rial Saidi at par in 1973.

The currency name was altered due to the regime change in 1970 and the subsequent change of the country's name.In AH 1390 (1970), a coinage for all of Muscat and Oman was introduced. Denominations were 2, 5, 10, 25, 50 and 100 baisa. In AH 1395 (1975), new coins were issued with the country's name given as Oman. 100 baisa, ¼ and ½ Rial coins in base metal were introduced for circulation in late 1970s and early 1980s.

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Source: http://www.chiefacoins.com