Dear Harendra
Unfortunately no university offers LLB through distance mode as its not recognised by Bar Council. But there are some other courses in the field of law -
1. Bachelor of Academic Law (Annamalai University - Distance Education)
2. LLB (Academics) {Guru Nanak Dev University - Distance}
3. Bachelor of General Law (Madurai Kamraj University Distance)
4. National Law School also offers distance courses in field of law
Besides above i have heard that Guru Jhambeshwar University, Kurukshetra University,& Jammu University also offers distance courses of law. You can refer sites of universities for details and other updates.
But remember, these courses will not be recognised by Bar council and you can't practice in court of law. But yes, you will definitely gain knowledge in field of law.
Regarding your portfolio Excise and Service tax you can refer following links of institutes offering specialised courses in these fields
TVC institute
https://www.tvcmumbai.com/
Indian Institute of Export Management
https://www.iiem.com/
I cant comment on credibility of these institutes and their courses. You have to analyze them as per your need. Any further update on above courses or any other related course is welcome.