Hi, I can't tell answer with much certainty with the information you've provided, so here are a few pointers for your investigation. Just before I get started, you're not trying to create the Content Fragment on the Publisher, right? I'm just asking because in your question you say "In an assumption its published, I have proceeded to create the "Content Fragment" under Assets>Files>Create -> Content Fragment" but:
- You should never create content on the Publisher, always create on teh Author and publish to the Publisher
- If you are creating on Author, then the publish status of the model really has no effect on whether you can create a Content Fragment from it or not

Moving on, here are questions you might want to ask:
Are you creating the Content Fragment from the right place?
You should have created your Model under a project folder (by default creating a Model at the root folder is disabled). You have to be in a folder with the same name in Assets in order to use your Models. Here is an example of what I mean (using We.Retail):

Has the Model even been published?
On your Author instance, go to Tools > Deployment > Replication
Here, click on Agents on author. You should see the following agent in the list:

If like me you have a warning about a blocked queue (in my case its because my Publisher instance ins't running) then your model never made it to Publisher. For more details, click on Default Agent (publish) and you can see what items are in the queue, test your replication and/or view replication logs.
Is the model present on Publisher?
You can't see the model in your Touch UI, but there anything in the JCR? on your Author instance, go to the CRX DE console (http://localhost:4502/crx/de/index.jsp). Find your model in the JCR tree, it should be at /conf/<your-project>/settings/dam/cfm/models/<model-name> or thereabouts (if you've created a custom folder structure, find it here).
Once you have the path, check it on your Publisher instance and see if it is present.
Try out these avenues and tell me how it goes
If it's not any of those at least you should be able to get an idea of where the problem might be.