I am planning to use adapter for dslr prime/zoom lenses from Nikon/Canon with Sony Mirrorless A7iii camera. Will this impact the quality photos taken? Will it be advisable to go for Sony E mount prime/zoom lenses rather than using adapter.
Using native lenses is bound to give you a better experience than with a mount-adapter. Assuming, an adapter that is purely mechanical - as most are - there will be no reduction in image-quality because all these adapters do is create space between the mirrorless mount and the flange distance for the DSLR mount.
Although image-quality is bound to be the same, the adapter has to be well built with tight tolerances or it could affect infinity or close focusing. Most importantly is that most such adapters have no electronics to control the lens, so you have to focus and set aperture manually. The big caveat is that some lenses lack an aperture ring and so it becomes impossible to shoot at anything but one aperture!
The are adapters that feature electronics to control the aperture but you have to check with the particular model what combination of lenses and body is supported. Even though you said Canon/Nikon lens, you will get better functionality with Minolta lenses because Sony makes their own adapters for them and the E-mount was built to supersede the A-mount which Sony acquired from Minolta who had merged with Konica. Note that Sony has 5 such adapters available and only 3 are compatible with full-frame cameras.