little think like finding how to RP social scenario if you do not pick bard your basically a loser, the martial being to support for the casters little things like that, the setting is more a matter of selling me on it as I find 90% of setting dull as dishwater so crazy would help.
I can provide several game options that provide social conflict systems as part of the core... but they're each different...
Mouse Guard - either edition - the conflict system is the same whether social, physical, or even ecological. What differs is which skills get used and the narration of the 4 moves (Attack, Defend, Feint, Maneuver).
Burning Wheel. Any edition. It's got one of the most realistic melee duels in print. It's also got Duel of Wits for social. And a ton of options. Note that Mouse Guard and BW are related; if you like BW, MG is going to be comfortable, and vice versa, but which is better is in how well one handles multiple subsystems.
Burning Empires is another BW variant - think Stargate's Goa'uld without the overt gloating, and hyperdrives but not gates.
Any of the 2d20 system games I've read have an extended task mechanic, and it's the basis for the physical combat. Use the combat methodology for social interactions, and it works fine. It's explicitly set up for social in STA and Dune, with very minor differences from physical combats in STA, and somewhat larger (but clearer) in Dune. Note that creating traits is one of the standard actions; this has been used for both informal and formal social encounters.
Most of the Year Zero Engine games can do social conflicts - but they don't make it explicit in most how. The basic idea is that one either does damage to mental attributes, or imposes conditions. Now, there are difficulties for such in the skills chapters, but it's not clearly labeled as social conflict.
There is social conflict in the FFG/Edge Star Wars system. It's not in the core, but the concepts are - damage is done to Stun, rather than wounds, and the victim run out first loses; the intent is for use in diplomacy, and it's in the Diplomat sourcebook for Age of Rebellion.
All editions of Legend of the Five Rings (which is a samurai fantasy) have abilities and skills to impose social effects; 5th (by FFG and now in the hands of Edge) actually has a stronger set, and it's nearly identical in concept to the one in Star Wars, given that it actually provides mechanics cogently. Still, many groups converged on the same proceses for social conflicts in 2nd and 3rd editions...
Cortex Plus and Cortex Prime games all have the ability to impose conditions upon foes... some flavors even have mental damage tracks... (MHR).
Likewise, all Fate games have the ability to create temporary aspects... these can be used to do social conflict as easily as physical... some flavors call this out.
Of those, which are a good fit for you is hard to predict.
Burning Wheel is robust... but it's also intimidating.
2d20 has large books... with lots of setting and fairly light rules.
Year Zero games vary widely, but basically all are count successes, with a risky reroll if the first throw on a task goes poorly but not horribly.
Cortex Prime is in print - the actual core is a construction set... adapted cores are being released. I've not seen those yet. Cortex Plus was largely the same as Prime, but each game was significantly adapted, and essentially incompatible.
L5R 5 is great, if one likes the custom dice. If not, well, then it's going to suck.
FFG/Edge Star Wars has the custom dice and difficulty as specific dice... you'll need two sets for more than starting characters...assuming one pool shared across a group. I keep 8 sets in my SW dice bag. (I'm currently running Edge at my FLGS.)