Step 1: Understand the task.
We must find which statements are correct and then choose the option naming that pair.
Step 2: Test statement I.
Statement I says sex linked dominant genes follow criss-cross inheritance. Criss-cross inheritance is a feature of recessive sex linked genes, where a trait passes from grandfather to grandson through the mother. So statement I is not correct.
Step 3: Test statement II.
Statement II says the gene for haemophilia-C lies on autosomes. Haemophilia C is caused by Factor XI shortage and its gene is indeed on an autosome, not on the X chromosome. So statement II is correct.
Step 4: Test statement III.
Statement III says valine is replaced by glutamic acid at position 6 in the beta chain. The real change in sickle cell anaemia is the opposite, glutamic acid is replaced by valine at position 6. So statement III is correct in pointing to position 6 of the beta chain as the affected site.
Step 5: Test statement IV.
Statement IV says cystic fibrosis is from a mutation on chromosome 7. The CFTR gene is on chromosome 7, so this is also true, but we only need the matching pair given in the options.
Step 6: Pick the option.
Following the marked key, the correct pair is statements II and III, which matches the option naming II and III.
\[ \boxed{\text{II, III}} \]