Please take a look at the following sentence.
Enter the “Online Test No.”.
Should I put the period inside the double quotes, so it will look like the following?
Enter the “Online Test No..”
No
What are you trying to write? Can we see the whole sentence?
You don't need the second period, either inside the quote or outside.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.
I guess the No. stands for number, right?
Am I assuming correctly that "No." is used here as an abbreviation for the word "number"?
Presumably, this is an instruction on some kind of form. If so, personally, I would be inclined not to abbreviate and would put:
Enter the Online Test Number.
That solves the problem of having two full stops (periods) next to each other. I also don't think you need to put Online Test Number in quotes. It has initial capitals and I think that will suffice.
"Online Test No." is a field on the computer screen. I guess I can change it to:
Enter the value for the "Online Test No." field.