I want to make my Lenovo Y520 duel boot, with Windows 10 Home, which it came with, and ether Fedora, or Ubuntu. It has two internal drives, a 250 GB SSD, and a 2 TB HD. I made a new 60 GB partition, on the SSD, for Fedora, booted the installer image, from a thumb drive. The live OS, and the installer would not recognize the partition I wanted to use. The same thing happened with Ubuntu. I tried turning off secure boot. That didn't help. I even tried deleting the partition, in Windows, in hopes that it would see the blank space, and be able to make its own partitions, no luck.

Did it see the SSD at all?

Have you tried creating the partition with an ext4 filesystem in it? You probably don't need to but that's what I usually do, using GParted Live, and it seems to work.

It doesn't recognize the SSD, at all.

Make sure you have the interface set to AHCI mode.

It's pretty rare that Linux doesn't recognize a SATA drive. Does Windows see it?

Yes, Windows sees it.

When it comes to storage, tools like lsscsi, lsblk and blkid are very useful. On the live OS, open a terminal window and try them. lsscsi lists all disks that look like SCSI (this includes SATA), lsblk lists all block devices, which includes partitions and disks, and blkid lists those block devices that contain a UUID.

Depending on the distro, you may have to run them as superuser.

In the same terminal window, also check for disk-related errors in the kernel message buffer, for example:

What is the output of fdisk -l, run as root. Be sure to surround it with "code" tags, which become available when you click the "Go Advanced" button beneath the "compose post" window.