Look it up on the Shop4parts website. They sell Fiat's own recommended Tutela oil which is what it gets in the factory.
I see above the old subject of GL4 vs GL5 raising it's "ugly" head. I'm very interested in lubricants generally and some years ago this was a very hot topic indeed with well founded claims that using the wrong oil could literally "wreck" your gearbox! A lot of the problems were caused by ill informed people learning that the GL5 formulation was better able to resist the sort of high pressure shearing forces experienced when the gears rotate in and out of mesh with each other (it was more "slippery" in layman's terms) and indeed this was/is true they are better able to maintain a layer of lubricant between the moving surfaces. Unfortunately the extreme pressure additives used are so good at adhering to the metal surfaces that the softer metals in the gearbox - bushings, synchromesh cones and the like (often referred to as "yellow metals") - would bond so securely to the lubricant that a very very thin layer of metal - talking at the molecular level here folks - would be torn off at each parting of the components. Very good for the gears which are far harder so don't suffer, very poor for the yellow metals which are slowly eroded.
The bottom line was that some gearboxes, and it depended very much on what their bushings and synchros etc were made from, quickly started suffering from "crashing" gear changes as you "swapped cogs". It was generally thought that the problem was due to the new GL5 oils being "too slippy" and thus "defeating" the synchros - I thought this for many years and I think there was a certain truth in this - but actually the big problem was simply that erosion of the cone faces of the synchros was reducing their ability to grip the gears and synchronize shaft speeds. So it was true that it was the GL5 spec oil, when used in a gearbox rated for GL4 oil, that was the problem but the reason was not what many of us assumed.
There is shed loads of info on the net about this problem but interestingly it now seems that the oil companies - some time ago actually - have realized that this is a problem and are using additives which are not so aggressive towards the "yellow metals" and some are producing product with almost the enhanced lubricating qualities of the more aggressive old type GL5 but using less aggressive extreme pressure additives. I think some are calling these GL4+ or GL4plus etc (the recommended TUTELA 75w-85 for my Panda is one of those and I use it in my boy's 2012 Punto too).
I've also read that these modified, less aggressive, formulations are now being used in GL5 so putting a GL5 rated oil in a box designed for GL4 should now be a much less risky thing to do. (but I wouldn't do it) Yes Fiat have see-sawed between GL4 GL4+ and GL5 in these boxes as at least a couple of the entries above have highlighted so it would seem that whatever metal FIAT are using for synchros etc is not dramatically affected by the GL5 but, as the spec has changed over the years then maybe only certain production runs used certain metals? Personally I'd not risk it. If in doubt I'd follow exactly what the manufacturer specified for that year and chassis number. If in doubt about one of the Fiats I'd ring S4p and get their recommendation as they seem to really know these things. I'd do this for any make and model of vehicle - use only the manufacturer's specified oil. After all it's only a couple of litres and probably only gets changed once or maybe twice in a vehicles lifetime so the slight extra cost is infinitesimal compared to the price of a gearbox repair or, maybe if you're unlucky, complete rebuild? By the way, I've said before, I don't believe in a "lifetime fill" for transmission oils. Any vehicle I own or is a family vehicle I look after, be it manual, and especially automatic, gearboxes, gets new transmission oil at around the 50 to 60 thousand mile mark and we haven't had a serious gearbox problem I can remember on a family car within my memory. The Astra is just coming up on 130,000 miles and running pretty well considering it's my boy's work hack and he treats it pretty hard. The Jazz, Panda and Punto are also well cracking on now.
Finally I have to say that this is all info I've uncovered by talking to people in the trade, motor factors, emailing oil manufacturers and searching the internet. I think I've got my facts straight but I may be wrong as I'm old and slow on the uptake. It's a fascinating subject and well worth googling to read what you can on it. If you discover something worth mentioning please do post and let us know, anyone?