a problem of PCIe on Cyclone V GT Dev Kit

You can in theory insert any PCIe device of any width into any PCIe slot of any width. During enumeration of the PCIe bus the width of each link is negotiated by sensing whether a lane is connected and functional at both ends.

If you plug in a PCIe x4 device into a PCIe x16 slot then during the enumeration process the PCIe switch or RC you've connected it to will detect that there are only four lanes and turn off the unused 12 lanes.