Dear Aspirant

Hope you are doing well

Now let me go through your question

No  this not such big mistake that why i think there should not be  any problem regarding it

because it's not like that your father's name is different or spelling is wrong on your caste certificate, it's just that there's no space in between the first name and the surname.

Still,

If you can get a new caste certificate made with space between first name and surname   then you should go for it otherwise you can use this caste certificate as well.

But please take some id proof yourself

And if you want to make any correction you go for it today is last date

And if you wanted to know more about it check out the link given in below https://www.google.com/amp/s/medicine.careers360.com/articles/neet-correction-window/amp