What is the role of Homocysteine in cognitive function?
I'm not sure if this answers your question, but I'll give it a try anyway. Here's a diagram of homocysteine metabolism. Vitamin B12 is a cofactor for homocysteine methyltransferase, and folic acid is required for tetrahydrofolate (THF). As both vitamins are involved in homocysteine metabolism, the symptoms of folate and vitamin B12 deficiency are similar. Vitamin B12 deficiency can result in neurological symptoms due to abnormal myelin, but folate deficiency does not. Vitamin B12 also metabolizes methylmalonyl-CoA to succinyl-CoA as seem here, so the methylmalonic acid level is often measured to test for vitamin B12 deficiency.

Hyperhomocysteinemia is the condition of high levels of homocysteine, but it is usually due to low vitamin B12 or folate.