Certainly the most important thing is not having symptoms. I expect that the reason for not having symptoms is that your dose of 200 mcg of Euthyrox is driving your Free T4 high enough to raise your Free T3 just high enough to relieve symptoms, even though you may not be converting all that T4 to T3 very well.
I would suggest that at next opportunity you should request to be tested for Free T3, along with the Free T4 and TSH. If the doctor resists, just insist on it and don't take no for an answer. Free T3 largely regulates metabolism and many other body functions. Scientific studies have shown that Free T3 correlated best with hypo symptoms, while Free T4 and TSH did not correlate at all. Since one of the very best measures of tissue thyroid levels is the ratio of Free T3 to Reverse T3, I also suggest it would be worthwhile to test and find out your Reverse T3 level.
As long as you are having no symptoms, I don't know of any big concern with your Free T4 level being above the range; however, if your doctor reacts to the low TSH and wants to reduce your meds, then you will need the results from the tests I suggested, in order to counter his intent by insisting that if your T4 dose is reduced, you want to add a source of T3 to your meds in order to keep your Free T3 high enough in the range to relieve hypo symptoms.
The only other suggestion is that if not tested previously for Vitamin D, B12 and ferritin, those should be done also, since hypo patients are frequently too low in the range for those as well.
Thanks. I feel fine, no any symptoms. I thought finally it's under control and was a bit surprised by the lab result.
*T.S.H (ultra sensitive): < 0.01 uIU/ml Adult 0.35-5.5
*Free T4: 2.0 ng/dl Adult 0.8-1.8
Not necessarily. Many hypo patients taking significant doses of thyroid meds find that their TSH becomes suppressed. This does not mean that you are automatically hyperthyroid, unless you do have hyperthyroid symptoms due to excessive levels of the biologically active thyroid hormones, Free T3 and Free T4.
So, before going any further, please tell us about any symptoms you are having and also post the reference range for your Free T4 test, as shown on the lab report.