iOS AVCaptureSession - How to get/set the number of frames per second recorded?

To set the capture session frame rate, you have to set it on the device using device.activeVideoMinFrameDuration and device.activeVideoMaxFrameDuration (if necessary).

In Swift 4 you can do something like this:

extension AVCaptureDevice {
    func set(frameRate: Double) {
    guard let range = activeFormat.videoSupportedFrameRateRanges.first,
        range.minFrameRate...range.maxFrameRate ~= frameRate
        else {
            print("Requested FPS is not supported by the device's activeFormat !")
            return
    }

    do { try lockForConfiguration()
        activeVideoMinFrameDuration = CMTimeMake(value: 1, timescale: Int32(frameRate))
        activeVideoMaxFrameDuration = CMTimeMake(value: 1, timescale: Int32(frameRate))
        unlockForConfiguration()
    } catch {
        print("LockForConfiguration failed with error: \(error.localizedDescription)")
    }
  }
}

And call it

device.set(frameRate: 60)

AVCaptureConnection's videoMinFrameDuration is deprecated.

You can use AVCaptureDevice properties to detect supported video frame rate ranges and can assign minimum and maximum frame rates using properties.

device.activeFormat.videoSupportedFrameRateRanges return all video frame rates ranges supported by device.

device.activeVideoMinFrameDuration and device.activeVideoMaxFrameDuration can be used for specifying frame durations.

Do it like this

if let frameSupportRange = currentCamera.activeFormat.videoSupportedFrameRateRanges.first {
    captureSession.beginConfiguration()
    // currentCamera.activeVideoMinFrameDuration = CMTimeMake(1, Int32(frameSupportRange.maxFrameRate))
    currentCamera.activeVideoMinFrameDuration = CMTimeMake(1, YOUR_FPS_RATE)
    captureSession.commitConfiguration()
}

You could use AVCaptureConnection's videoMinFrameDuration accessor to set the value.

See the AVCaptureConnection documentation

Consider output be AVCaptureVideoDataOutput object.

AVCaptureConnection *conn = [output connectionWithMediaType:AVMediaTypeVideo];

if (conn.isVideoMinFrameDurationSupported)
    conn.videoMinFrameDuration = CMTimeMake(1, CAPTURE_FRAMES_PER_SECOND);
if (conn.isVideoMaxFrameDurationSupported)
    conn.videoMaxFrameDuration = CMTimeMake(1, CAPTURE_FRAMES_PER_SECOND);

More info, see my answer in this SO question