I'm a writer so I think I can provide a few insights on this. But to clarify, by beloved do you mean,
a) a strong relatable character?
b) a well built realistic character?
c) a lovable character whom everyone likes?
I ask this because a strong fictional character is not exclusively a very happy very loving one that everyone roots for. Sometimes the bad guy, the evil lady, the ruffians and the thieves might be the character that elicit the strongest reactions from us. Even if that reaction is hate.
I will try to explain to my knowledege how a character like this may be created. Also if what you're referring to is the latter, i.e a lovable character whom everyone fawns over, I will also try to elaborate on means by which that can also be achieved.
First of all, we must identify what makes any work of fiction thrive, what makes the reader stay engrossed and keep reading, and this is CONFLICT. A conflict is a situation that provides the impetus and the action. Let us keep this in mind for now.
The first thing to do in creating a character is the identification of traits. I.e is the character male or female, tall or short, white or black, pink or yellow? (lol)
Note that having identified your character traits in your mind, you do not have to bombard your readers with all the details, but only the ones important to the plot. Ernest Hemingway refered to this as the Iceberg Theory.
Now having set your character in your reader's mind, a way to make them lovable or admirable is to give them traits that conform to conventional goodness and beauty. Lovely eyebrows, charming smile, blue eyes, great hair etc. But all these, it still should be said, are only by the way and are by no means the important part.
The important part is where the conflict comes in. The part where you throw your characters into a conflicting situation. A situation that sets a challenge for them and mostly require them to make a decision. Examples of conflict in books and movies might be the part where a lady chooses between two men in triangle romance; the part where a dragon attacks in fantasy, the scene where Daisy had to choose between Gatsby and Tom Buchanan in The Great Gatsby.
In all these cases you'll notice there are also characters and elements that bring about the conflicts, but that is a scope of discussion for another question entirely.
The important thing, however, as I was saying, is the part where your character makes the decision. This is important because most of times the fate of the character, not only in the fictional word but also in real life with the audience, depends on this. This is where your character can be shown to be lovable or sinister.
Another good advice when creating characters is to make the character with relatable traits so as to inspire verrisimiltude but never to make them respond to situations predictably. Make him or her do and say things that are totally peculiar and unpredictable. This way even a sinister character may be admired for his or her uniqueness. Trust me, uniqueness is a trait valued by even the greatest pessimist.
Another area you can work on is the aftermath of the decison. Here you can switch things up and introduce a PLOT TWIST. Remember the story is ultimately yours and you can choose to steer it in any direction YOU want. You can choose to make the seemingly good decision turn out the bad one. You can make the seemingly innocent character turn out absolutely evillllll; the evil one you can make to turn out good.
This is a form of what is known as CHARACTER DEVELOPMENT, which is one of the most important part of fiction writing.
Then comes your DENOUEMENT or resolution, where the pieces are then restored and peace falls upon the city once or more, or if there's no chance of peace, at least the storm is passed and the characters have the chance to live on in the audience's mind.
Hope I've managed to answer your question satisfactorily.
Cheers.