No.   
They use different connectors, different rules to activate and refresh the stored values, and different voltages, so even if someone could make a physicall adapter, they still would not work.

DDR3 for desktop and server PCs use a 240 pin connector.

DDR4 for desktop and server PCs use a 288 pin connector (not 260). [Source1][1] [Source 2][2] [Micron data sheet][3]


  [1]: https://www.wepc.com/reviews/ddr3-vs-ddr4/
  [2]: https://www.bestsevenreviews.com/ddr3-vs-ddr4/
  [3]: https://www.micron.com/-/media/client/global/documents/products/data-sheet/modules/unbuffered_dimm/ddr4/asf9c512x72az.pdf