Obviously Ampere GPUs are slowly to replace anything based on Turing over the months to come, but it seems that the first laptop GPU already has been photographed, the mobile RTX 3070 version that is. it however would be the same chip used for RTX 3060 Ti and 3070 on desktop.
The photo below got posted Chinese forum. Visible are an Nvidia chip with the inscription 'GN20-E5-A1' and eight memory modules from SK Hynix. The product code on the GPU would refer to the GA104 chip, the same that will also be used in the desktop variant of the RTX 3070.
This confirmed that GeForce RTX 3070 Mobile has GDDR6 memory as the SK Hynix modules are labeled H56C8H24AIR. A Google search reveals the AMD Radeon Pro 5500M uses the same memory.
In terms of capacity, according to Notebookcheck , the RTX 3070 Mobile which is codenamed GN20-E5 should have 8GB GDDR6 memory on a 256-bit bus. Note that the full GA104 GPU has 6144 CUDA cores, but the RTX 3070 Mobile will be a scaled-down variant, so we cannot confirm its specs yet.