That's almost certainly, a DWM manufactured 'contract Mauser', Brazilian Model 1908. Many South American, central European, and Middle Eastern countries had no arms manufacturing industries, so bought their weapons in from German (Mauser and DWM), Austrian (Steyr) makers. After WW1 when Germany / Austria were stripped of their arms industries by the allies, this function moved to FN (Belgium) and CZ/BRNO (Czechoslovakia).
DWM was Deutche Waffen und Munitions Fabriken, a merger of Ludwig Loewe and others, and in turn taken over by Mauser in due course. It was based in Berlin and made Mauser rifles under licence. Such small / medium sized armies' work was very lucrative and the manufacturers would make considerable numbers of modifications to suit customers' requirements and whims, so stocking, calibres, sling and stacking swivel positions, and especially sights varied between models, although they were all based on standard German / Austrian designs, primarily the M1889 Belgian rifle, M1893 Spanish, and M1898 German service rifle models depending on when ordered. Customers demanded and received very high standards of manufacturing precision and overall metal and woodwork finish, and national crests were usually incorporated into the action front reciever ring.
Unsurprisingly, those rifles ordered after 1900 were all based on the latest German model, the Gewehr 98, or M1898 as it's often called, until the AK47 appeared, the most manufactured and copied rifle in existence and the zenith of the late 19th, early 20th Century bolt-action rifle design. The M1908 was a modified G98 retaining its action, straight-out bolt handle, and long barrel, but with a tangent rearsight replacing the complex 'Lange' model of the German model. It was made in 7X57mm calibre, a cartridge originally developed by Mauser in 1892 for Spain, and widely used by several South American countries (by Brazil until the 1960s including in FAL assult rifles). Alongside the long rifle, there was a short rifle, and even shorter cavalry carbine also in 7X57mm.
7X57mm ammo is still widely available as are components for handloading, so your M1908 is still 100% serviceable if its bore is good. It's also a popular shooter / collector piece, and while not incredibly valuable will command a fair price if mint. Large numbers were imported into the USA as surplus rifles in the 1980s / 90s. They are rare in the UK as we saw very few come our way and people ask £700 - £900 here for a good one, but I'd imagine they're a lot cheaper in North America. Havcing an original bayonet (and sling if that's there too) enhances its value to collectors.
If you want to find out more on the rifle, there are many excellent textbooks on Mausers, and you can look up the M1908 Brazilian Mauser on Wikipedia etc. If you want to shoot it, have it checked out by a gunsmith and you can buy factory hunting ammunition in the calibre without too much trouble, several firms still producing it.
You have an interesting piece of history there - well worth hanging onto IMO.