What are the ways of creating Subplots in fantasy genre that really catch the reader's attention? Should there be a conflict in the subplots? Please explain.
As you introduce the main character to the world, you will also introduce all kinds of other characters that interact with this MC. You introduce your setting, your world, your universe.
And sometimes the universe you create is so large that all kinds of things happen even while the MC is not around. Some of those things might eventually even become relevant to the MC at some time in your story.
You have to build up to those relevant things. And this build up will be your subplot until eventually it becomes part of the main story line.
To answer the question. Is there conflict? I sure hope so, otherwise the subplot will be tedious and boring for the reader. And how do you keep the readers attention to the subplot? Make it relevant to the main plot line.
A subplot is basically another story included inside your main story, one that is simpler and less detailed than your main storyline. It does need some conflict in order to be interesting, but this tends to be both less complicated and more easily resolved than the conflicts in the main plot. There can be many reasons and ways to deploy subplots, but the two main types of subplot are ones that illuminate the main plot, and ones that interact with the main plot. I'll use the 2001 movie Monsoon Wedding as an example, it uses both effectively.
REFLECTIVE - To illuminate (echo and/or contrast with) the main plot: This kind of subplot is largely separate --in a causal sense --from the main plot. It might even be a story or a anecdote told within the main plot. However, it has aspects that illuminate some feature of the main story, by both echoing it and contrasting with it. For example, in Monsoon Wedding the main plot is about a woman falling in love with a fiance she barely knows, just prior to a lavish arranged marriage. But there is a memorable subplot about the wedding planner falling in love with the family's maid. The echoes are clear, both are love stories, culminating in a double wedding at the end. But there are also contrasts. One couple is rich, the other is poor. One love affair is arranged, the other is spontaneous, and so forth. The existence of the subplot deepens the emotional content of the movie --the love of the second couple is purer and less complicated than that of the first couple.
FUNCTIONAL - To interact with (advance or complicate) the main plot: The main overall plot of most movies and books could be summarized in a few paragraphs --they aren't that distant from the fairy tales and myths that compose the primal materials of storytelling. It's the functional subplots that give the story its unique shape and structure. For instance, in Monsoon Wedding, the family throwing the wedding must make a stark moral choice around rejecting the much needed financial support of a wealthy family member, who has secretly abused a young member of the family. This choice becomes a major functional complication in how the movie is going to resolve -- it has real consequences for the family, either way.
I tend to think of subplots as being 'small plots that serve the main plot', and they can serve in many ways. It can be dealing with an aspect of a main character's personality that needs to change to allow the plot to continue, it could be to set up a situation that leads to the next major hurdle on the quest's way, heck it could be simply to establish something about the main character/villain.
As J.G pointed out, regardless of function, subplots often arise organically; the world of your story exists, and in transit, obstacles arise because that's how the world would work, simple as that. Then the only duty you have is to make said obstacle interesting.
I'd add on to Totems Maximus' answer to say:
Subplots can be the Goal and Arc of a secondary character, or of multiple secondary characters.
Samwise's goal was to protect Frodo. Gollum's goal was to get the ring. Both of those impact Frodo's goal to destroy the ring.
Each character has motivations and goals--and these can be developed up into side-stories. If LoTR was written from Gollum's perspective, the main plot and subplots would shift around. You could write the story from any LoTR character's perspective--the Nazguls, Eowyn, whoever--and the plot and subplots would shift.
I find this a useful way to think about subplot. Your secondary characters are not mere window dressing but people in their own right.