Step 1: Characterise the syndrome. Ataxia-telangiectasia, also called Louis-Bar syndrome, is an autosomal recessive neurodegenerative condition combining cerebellar incoordination with dilated small vessels and a defective DNA-repair system.
Step 2: Pick the true statement. A reliable marker of the disease is raised serum $AFP$ (alpha-fetoprotein), so the statement about increased AFP is correct.
Step 3: Round out the picture. The faulty DNA repair drives a high risk of haematological malignancies, especially lymphoma and leukaemia, and patients also show oculomotor apraxia, dysarthria, and immunodeficiency with frequent infections.
Step 4: Knock out the false claims. The malignancy risk is lymphoreticular, not squamous cell carcinoma, and the inheritance is recessive rather than dominant, so only the AFP statement survives.
\[\boxed{\text{Increase in AFP}}\]