Oil in the ground is found under the oceans and seas. It is made of dead fish. But from what period are those fish? I heard they are about 119 million years old. But fish exist much longer than that. So is it clear how old our oil is?
Oil can be generated from pretty much anything organic. The oldest oil that I know of comes from a porous Eocambrian siltstone in the Sultanate of Oman. This was formed nearly 200 million years before there were any fish around. Apart from that, oil can be formed in any of the geological eras up to the late Cenozoic.
The previous answer is actually correct in stating that fish have very little to do with oil formation. Hydrocarbons of a volume that is able to accumulate a reservoir that is economic to produce requires significantly more source material. The greatest volume of material that is a viable source of hydrocarbons is zooplankton, those tiny little things taken collectively represent massive sources of material which can be converted to oil and gas. There has been a misrepresentation in the media that vertebrates are a source of oil and gas, but the volumes are just not balanced, the amount of oil available requires a massive source material, and the available area of the ocean, and short life cycle of zooplankton provide the proper volumetric balance. Phytoplankton are also have tremendous volume, but the material lacks the amount of oil source material to provide for significant contribution, more waxy than oily.
The previous answer indicates that the oil is in the sedimentary fans, and the source is from the rivers, this isn't true. The typical oil source rocks are organic black shales, and the oil and gas migrates after maturation to a reservoir where production can take place. There are a whole host of issues that can happen along the way that are either positive or negatives for accumulation of a viable reservoir.
Look up the oil production pathway to learn more than you ever wanted to know...the basics are, a source rock that spends the proper amount of time at the maturation temperature, then the primary migration from the source rock must occur, leading to a reservoir with characteristics that allow for production, porosity and permeability, a trap and seal. The previous answer is describing potential reservoirs not sources.
Recent advances in hydraulic fracturing, which is an old process with new capabilities due to advances in drilling and production techniques allow for production from source rocks that have generated large volumes of gas that has not been able to migrate from the source into a reservoir where conventional production would have been used. Opening migration pathways and controlling the pressure in the source allows the gas to change phase and release from the source through the created pathways to the well for production.
kwinkunks comment is right, vertebrates don't contribute to oil formation in any significant way.
I think that fish actually contributed very little to the oil. Oil is typically found in current or former sedimentary fans of rivers and other basins where sediments were deposited. The Gulf of Mexico off the Louisiana and Texas is a good example, as it represents the sediments transported into the ocean by the Mississippi (and whatever rivers and basins came before).
What is later converted into oil is then simply the organic matter that is transported by these rivers and deposited in sediments together with sands, silts, and other inorganic matter. The latter compacts into sandstones and other reservoir rocks. The organic carbon is most likely largely from plants and bacteria, because their overall mass is so much larger than that of animals (including fish).