It has eggs like Wyvern and Rock Drakes. All you need to do is find the eggs. The only thing I know location wise is somewhere in a lava cave there is a tunnel with purple crystal on the walls and ceiling. When you go through that tunnel there is a large room with a lava lake in it. There will be lots of Magmasaurs in the room guarding the eggs. Note that the eggs are on the surface of the lava, so you might want to use a flying Dino and a grappling hook.
I’ve found the eggs. The eggs are located inside the volcano in an amethyst cave. There are lava pools with groups of magmasaurs in them. There are small islands with craters in them, within those craters the eggs are nestled within. But be careful there are lots of magmasaurs, magma, and what look like varient rock elementals.
When raising Magmasaurs, you can incubate their eggs with either standing torches, dimetrodons (level melee only, it increases the incubation effect), air conditioners or a combination of all of the above. It takes a LOT of heat.
They eat Ambergris which can easily be mined from the lunar biome with an Anky (for the best yield).
Higher level Magmasaurs are best to raise, they have better food value.
At the “Juvenile” stage when they can be on trough, you can put their food (Ambergris) into a trough which helps with raising multiple tames (or bring over a character that has Tek unlocked and use a Tek Trough to preserve the food). (I play Xbox official).
Low level Mags might not look like they are taking food from the trough if their food value is low. Watch them and see if they eat once the value reaches zero. Higher levels do better for some reason. This knowledge might save someone some sleep. :-)