F1 to H1B, first time stamping, asylum denied when on F1

[Engineer20]

I have been on F1 for 6 years and on the first year had my asylum application denied. I am from an African country. I continued on to finish my degree and have been on an H1B for a year with 2 more years on my approved petition. Now, I have to travel for work to India ( for less than a month) and thus have to apply for an H1B visa stamp. I have never left the US since i first came (7 years). My question is if or how my denied asylum application can affect my H1B stamping request? Also, would it be advisable to apply for H1B stamping in India as a third country national (TCN)? I no longer fear persecution in my country and thus i am able to go if i want.