Show a folder as virtal hard drive

You can share these folders and then map them as a network drive.
Or you can create hardlinks to your mounted F drive for that folder.

thx for your answer, can you tell me how to do that?

For sharing: right click on a folder - properties - sharing tab.
Share it and note the path.
Then right click on This PC and select Map Network drive. Show the path to your shared folder.

For redirection through linking: http://techgenix.com/folder-redirections-in-windows/ 
Follow the instructions here.

Use the Subst command

subst f: d:\myfolder

Select allOpen in new window

Subst command should be rerun after each new start as far as I remember it. In form of bat file in startup.

I tried both methods thx guys, however both methods didnt worked as expected :(, i will explain more:
I am have program which lists my hard drives (c,d,e,f), I created the drives which points to the folder in the above methods and i see them in "This PC", however when I load the program, these created logical drives didnt shown on the drives list.
I go to computer management and created a vhd drive and assign a letter for it, it appears in the program.
What I want something like vhd, but it reflects a folder content

If the VHD is mounted permanently then link the folder to it. Does it allow you that?

Didnt worked, the logical drive like vhd should directly refering to the folder

Strangely for me it works. I used Mklink /J F:\redirect G:
where F: is my mounted VHD file and a redirect folder was created on it. Then I manually created a folder called redirect on G: drive and put data into it. The data appeared in F:\redirect folder immediately.
Maybe it won't work with your app but I don't know what kind of app it is and what it is doing at all.

I tried the solution too but didn't work,
The application I am using is Backblaze, which backup my the hardrives to the cloud (without the ability to select just a folder)
What I want to achieve is to have a virtual drive "B" example which is pointed to my drive g:\mydirectories\forcloud" so only the files and folders in the for cloud folder will be backed up to the cloud

If the agent of that software is capable of backing up the content of virtual drive B then what I am referring to must work. Before physically the data is on B and not in original folder.

you will have to check with the manufacturer (backblaze) they probably query the disk hardware itself i.e. what you can see in diskmgmt.msc or diskpart