Is there a Filter Pair which fulfil both the Nyquist criterion and the Matched Filter Criterion?

Yes, there are filter pairs that fulfill both the Nyquist criterion and the Matched Filter Criterion. In fact, the Raised Cosine filter is a commonly used filter that meets both criteria. It is a popular filter in digital communication systems for its ability to minimize intersymbol interference while maintaining spectral efficiency. Other filters that meet both criteria include the Root Raised Cosine filter and the Gaussian filter.