After 1 month on zoloft (sertraline) for anxiety and depression i found i have vitamin b12 deficiency (blood test), can this solved by supplements or its permenant?

Your body doesn't: make vitamin B12 so you need to get it from animal-based foods or supplements. It is something vegans/vegetarians need to be especially mindful of. Conditions which impair absorption also contribute: atrophic gastritis (thinned stomach lining), lack of intrinsic factor (pernicious anemia), GI surgery, small intestinal disease, heavy drinking,etc. Most often, supplements needed lifelong. Stay well!

It depends: B12 deficiency is treated by taking B12 supplements. The underlying cause determines wether it will be permanent or not. Some causes, such as Pernicious Anemia(an auto-immune disorder) or post gastrectomy state are permanent. Other causes of B12 deficiency can be cured/corrected: H.pylori infection, adverse effect of prolonged H-2 blockers or PPI's etc.

Easy treatment: B12 deficiency is easy to treat, usually with oral supplements but injections sometimes needed. It is also important to try to figure out why you are deficient in B12. No relationship to the zoloft, (sertraline) however.