Serbia didn't use Mosins primarily, although they had them. The Mauser is actually what you would be most likely to find.

The Mauser Model 78/80 was a single-shot, bolt-action rifle firing a black powder 10.15x62.8mm round. It was a variation on the Model 1871 Mauser, and adopted (obviously) in 1880, only two years after independence. It was soon supplemented with the Model 1884 "Koka", also 10.15mm, but a repeating bolt-action rifle with a tubular magazine. I don't have production numbers for the 78/80 (quite a few built I believe), but with the "Koka", 4,000 Carbines for cavalry were built, with a 5-round magazine, and another 4,000 slightly longer "Short Rifles" for artillery units were built with 6-round magazines. These were contract Mausers, meaning they were built by Mauser at Obendorf for Serbia. Although supplanted by later arms, you could still find some being issued well past World War I.

Firing a large-bore round though, these were not modern rifles come World War I, and had been replaced for frontline service by a few more recent developments. First came the Serbian Model 1899 Mauser, a copy of the Chilean Model 1895, and like the Chilean, chambered in 7x57 rimless, a pretty uncommon round (in the interwar years, remaining stocks were rechambered for 8mm Mauser, known as the M1899C). These introduced a 5-round box magazine, which was by now a standard Mauser feature. Again, these were contract Mausers, with ~90,000 built in Germany by DWM. Not nearly enough rifles - keep in mind that roughly 420,000 were mobilized in 1914 - a further order was contracted through Steyr in Austria in 1907, called the Model 1899/07. There are some minor improvements, but they are essentially the same rifle. A shortened Carbine was produced as well, known as the Model 1908, but in rather small numbers.

Still with woefully inadequate rifle stockpiles still - far too many were still carrying those blackpower M1880s - a new order was placed, for the final pre-war model Serbia adopted, which was the Model 1910, produced at Oberndorf again. With a mix of features, it was sort of the bastard love child between their Model 1899 and the famed Mauser Model 1898. It chambered in the Chilean 7x57 rimless, and post-war 8mm Mauser converted stocks are the Model 1910C.

Now, thats what the Serbians would have been officially armed with. But lacking a domestic industry and buying all your pre-war weapons from your now enemy (Germany and Austria-Hungary) is a really bad combination when you go to war, especially when you already have supply issues from the get-go! The result of this is that aside from their Mausers, Serbian soldiers carried a wide array of foreign surplus supplied to the by their allies, especially the French and the Russians.

From the French, you would find Lebel 1886/93 Rifles and Berthier rifles and carbines (there are a number of variants). From the Russians, you would of course find the Model 1891 'Three-Line Rifle', aka the Mosin rifle, as well as the older Berdan M1870 rifle, a single-shot blackpowder gun, but somewhat better than nothing. I don't know of the British, Italians, or Americans providing any of their arms, but of course just because I don't find reference doesn't necessarily mean they didn't.

Sources

Mauser Military Rifles of the World - Robert W.D. Ball

Bolt Action Military Rifles of the World - Stuart C. Mowbray and Joe Puleo

Standard Catalog of Military Firearms, 7th Edition - Phillip Peterson

Armies in the Balkans 1914-18 - Nigel Thomas and Dusan Babac