Have you tried to use MediaProjection API to achieve this. I suggest to look along the following code. For more information about the API refer this.
//You have to start the Screen Capture based on an action.
//mWidth, mHeight depends on device screen width, height
mImageReader = ImageReader.newInstance(mWidth, mHeight, PixelFormat.RGBA_8888, 2);
mVirtualDisplay = sMediaProjection.createVirtualDisplay(SCREENCAP_NAME, mWidth, mHeight, mDensity, VIRTUAL_DISPLAY_FLAGS, mImageReader.getSurface(), null, mHandler);
mImageReader.setOnImageAvailableListener(new ImageAvailableListener(), mHandler)
startActivityForResult(mProjectionManager.createScreenCaptureIntent(), REQUEST_CODE);
//Then convert the media captured to an Image
sMediaProjection.stop();
image = mImageReader.acquireLatestImage();
Image.Plane[] planes = image.getPlanes();
ByteBuffer buffer = planes[0].getBuffer();
bitmap = Bitmap.createBitmap(mWidth, mHeight, Bitmap.Config.ARGB_8888);
bitmap.copyPixelsFromBuffer(buffer);
File file = new File(Environment.getExternalStoragePublicDirectory(Environment.DIRECTORY_PICTURES), "SNAPSHOT.jpg");
fos = new FileOutputStream(file);
bitmap.compress(CompressFormat.JPEG, 100, fos);
fos.close();