Anksthakur, the information you have given is about two different things. The cartridge marking is for 50 Eley Express, otherwise termed 500 Express. This is a very long cartridge that will only chamber in a single shot rifle. This would indicate that the rifle in question is something like this one:
https://www.rockislandauction.com/detai ... ress-rifle
because you state that the rifle is a Winchester. This is the only Winchester that the 50 Eley Express would fit, as the 1886 lever action Winchester is far too short to chamber such a cartridge, and the cartridge is too fat.
The cartridge you are speaking of, the 50-110 Winchester, is intended for the Model 1886 lever action gun. Looking at the base diameters of 50 Eley Express and 50-110 Winchester, it is more than possible that firing a 50-110 cartridge in a rifle chambered for 50 Eley Express would split open and pour hot gasses in your face. (May I observe that, from personal experiences, this is NOT an enjoyable event!) Furthermore, the difference in the rim diameters of the two rounds makes it unlikely that the extractor of a 50 Eley Express rifle would extract a 50-110 cartridge.
The bottom line here is that firing a 50-110 cartridge in a rifle intended for 50 Eley Express is dangerous and not very useful, although no doubt there is some individual who has done it somewhere at sometime.
Now, for ammunition:
50-110 is somewhat available in the USA. It isn't loaded by any of the large commercial ammunition companies, but would be available from smaller semi-custom and custom concerns, such as Buffalo Arms.
https://www.buffaloarms.com/50-110-winc ... 10win.html
Regarding 50 Eley Express, I suggest that you read this article:
https://www.riflemagazine.com/the-big-50
And then consult this page:
https://www.buffaloarms.com/ammunition/ ... er-up.html
The bottom line:
For such a rifle as a Winchester Model 1885 Single Shot in 50 Eley Express, you are looking ammunition costing between $7 and $10 a round. How and how much it would cost to get this ammunition in India is anyone's guess; I don't know about that. If you want this rifle to shoot, you need to either be a very wealthy person (money always finds a way, doesn't it?) or be a reloader, and it would not be especially cheap to reload for 50 Eley Express, either, if you could get the components to do so which, in India, you probably can't. You can't even get components in the USA anymore!
I'm sorry to be the bearer of dismal tidings to your request, but there it is.