Some graduates and students do job-oriented courses or internships by paying a fee. Under which section of a resume should these job-oriented training / internships be mentioned?
It should be listed under Education
Education is anything that educates you. It's not only for degrees or diplomas. For example, I graduated from a military school. There was a piece of paper added to my military record, and no diploma or certificate that I could show an employer. I list it under Education.
Online courses that you pay for, they can go under education. Online course that you don't pay for can go under education. Trade schools can go there. Mentoring relationships can go there. I've seen people list what High School they went to. I've seen people list unpaid, non-attendance taking, volunteer courses which didn't even have exams (that I taught) there. Anything where you learned something can go there, if you want to mention it.
The only reason you don't list some kinds of education there is because you feel that if you listed stuff too trivial, then it would raise more questions in the minds of the people reading your resume than you wish raised.
Yes, it's completely normal to mention this. It's a non-issue: have a line in your cv mentioning this.
You mention for example "bootcamps". Similarly, it's completely normal to mention those in a line in your cv.
Say nothing about whether it is paid, unpaid, or anything else.
(Obviously) openly state the actual name of the institution/facility. Everyone in your industry will know all about it.
It's a non-issue - put it in a line in your cv.
"... under which section should it be listed?"
Folks glance at cvs for a second or less. (I would suggest not even having "sections" on your cv! It's completely obvious what each item is.) Put it under education, since it's a course.
What about having a new section heading, "Courses"
"But they don't offer any degree or diploma, so they can't be considered as education institutes..."
That's wrong, any number of courses (you refer to it as a course) don't specifically offer a diploma or the like.
Put it under "Courses".
Again, everyone in your industry will instantly know what it is, nothing to worry about.