Note that some models of those do not work with 720K sized diskettes. The models of mine that I have listed here, work with both 720K and 1.44M diskettes.
Depending on the vintage of your old PC, you may be able to simply connect a 3.5" diskette drive to its floppy controller card.
In some cases you can fit a 1.44M sized 3.5" diskette drive, but you'll be limited to using 720K sized diskettes.
Use a floppy controller that contains its own BIOS, a BIOS that supports 3.5" diskette drives.
The one pictured below supports four drives, in any combination of 360K/1.2M/720K/1.44M
For this controller, minimum DOS versions apply (e.g. at least DOS 3.3 required for 1.44M drives).
Using this card on a IBM 5160 motherboard, unless the motherboard's BIOS revision is the first one (11/08/82), I cannot boot from known good 1.44M sized MSDOS boot diskettes. Reading is fine; just cannot boot.
Pictured below is what is generally referred to as a 'parallel port 3.5" disk drive'. As the name suggests, it plugs into the PC's parallel port. These appear periodically on eBay.
To work, they require a driver. In DOS, that driver is typically loaded via CONFIG.SYS
Booting from these types of drives is not possible.
The particular drive pictured below is a Backpack model 014350, made by Micro Solutions. The DOS driver for it is designed so that the Backpack 014350 can even be used with 8088 based PCs (such as the IBM PC and IBM XT). Click here to see the flyer.
For 8088 based PCs (such as the IBM PC and IBM XT), the use of 2M-XBIOS software and a 16-bit floppy controller.
Click here for more information.