Expert class

What is your approach for using skills in combat ?

Otherwise, is anyone has other ideas for a expert class if my raise system is not fine ?

Here is a short workflow for how I design Homebrew:

1) Determine the problem or limitation you want to solve. In this case is it :
A: the lack of ability to use skills in combat? 
B: the lack of a class specializing in being good at skills? 
C: the low value players & DMs put on skills ?

2) Flesh out the details of the problem.
A: if this is the problem, should all characters & classes be able to use skills in combat or only certain characters? Should it be possible to complete a combat (i.e. kill enemies) exclusively using skills?
B: if this is the problem, then what is missing from the Rogue or Bard class? Why don't they feel like they specialize in being good at skills? Does this class need to be combat-oriented or is being good as skill out-of-combat sufficient? 
C: is this is the problem, then is it that skills need to be more reliably successful in general? Do they need to be able to do more things? Do they need to be as powerful as spells? 

3) Consider existing solutions or similar mechanics in D&D or similar TTRPGs. Can they be co-opted? If not where do they fail?
Pathfinder has a whole set of combat-oriented skill actions, which is what I based my suggestion on.
Pathfinder also has a class the Swashbuckler who put a big emphasis on using skills in combat.
Pathfinder also has special combat actions that combine attacks & skill checks.
There are other RPGs that have a whole parallel combat system that focuses on using skills to wear down the morale or stamina of the enemies rather than their health.
D&D has the Maneuvers system in the Battlemaster which is meant to mimic using weapon skill in combat, which could be co-opted for other kinds of skills.
D&D has Monk subclasses that use Focus Points to create spell-like effects that is supposed to reflect using skill & wisdom to achieve supernatural effects.
D&D also has the Rogue and Lore Bard as skill-focused classes, and the Artificer as a mechanical / crafting skill focused class.

4) Decide on what kind of homebrew you are going to make to solve the problem, and which kinds of mechanics you are going to borrow from / be inspired by to build it.
Do you need to make a full class, one or more subclasses, one or more feats, or a class-agnostic game system? 
Is it going to be a supplementary activity driven by some kind of resource with a recharge mechanic or an always available default mechanic?
What existing rules in D&D is it going to use? spellslots? conditions? bonus pools of dice? weapons / equipment? Adv/DisAdv?

5) Use the most similar mechanics already available within D&D to determine the appropriate balance for the homebrew. 
e.g. if it is a homebrew class, compare the expected damage output per level to that of a Rogue's Sneak Attack or a Warlock using Eldritch Blast. If it is a homebrew subclass, compare the power of the abilities to those of the other subclasses of that class at the same level. 

This thread was created to discuss something that I feel is missing from D&D. I think it's unsatisfying that succeeding on a skill check by 0 or by 20+ often produces the same result (unless the DM is willing to improvise). That's why I didn't present a finished product—only a rough concept meant to explore the idea.

Pathfinder essentially uses the same approach as D&D, except that it expands it with critical successes and critical failures. That's an improvement over having only a binary success/failure outcome, but I still think it's less nuanced than my proposed "raises" system, which allows for multiple levels of success instead of just one threshold.

 I think it's unsatisfying that succeeding on a skill check by 0 or by 20+ often produces the same result (unless the DM is willing to improvise). 

What is specifically unstatisfying about that? Do you feel the same way about saving throws? Succeeding a save by +20 or +1 doesn't change the effect. Same goes for attacks. If those don't feel unsatisfying consider why? What is it about ability checks that makes succeeding by a lot and not getting additional benefit unsatisfying?

Then consider the contexts skill checks are made in. They are used in all kinds of situations from jumping across a chasm, to climbing a tree, to discovering a clue, to picking a lock, to convincing an NPC to help you. Does it always feel unsatisfying to have a binary outcome? Or only in some cases? 

Are you specifically talking about using skill checks in combat actions - like swinging from a chandelier before making an attack - or also out of combat - like jumping over a barrel of mead to impress some NPCs in the tavern?

What specifically is the issue you are trying to fix? Is it combining skills with weapon attacks in combat to do "cool" action-movie stuff? Is it being able to use skills instead of attacks in combat to have like a super skilled character who doesn't swing a sword or fling spells still be an effective character by talking down the enemy or coming up with strategies or using tricks to defeat the enemy?  Is it being able to do more supernatural-level stuff outside of combat like spells can do but without using magic? 

Note: the D&D DMG has multiple levels of success as an optional rule for running skill checks. In my experience most DMs do run multiple levels of success when it comes to information gathering, as well as social interaction checks.

PS If it is just grades of success you are after, then you could simply make a general mechanic as follows:

Grades of success

When a player character or other creature is makes a d20 roll compare the result to the table below:

10 or more Below the DC : the creature is humiliated by its failure, it has Disadvantage on the next d20 roll it makes and takes the penalty from the previous failure conditions.
5 or more Below the DC : the creature takes damage equal to the amount it failed the DC from a catastrophic accident during their attempt, and the penalty below.
1 or more Below the DC : the creature fails and takes a -2 penalty if it tries to repeat the task (i.e. making another attack against a creature, or repeating a save against a spell).
MEETS THE DC : success no other effects
1 or more Above the DC : the creature succeeds and gains a +2 bonus to the next d20 roll of the same type (e.g. if it was a Dex save it gains a +2 to the next Dex save it makes) within the next minute.
5 or more Above the DC : the creature doubles the effectiveness of their attempt - if it was an attack they deal double damage, if it was a saving throw vs half damage they instead take 1/4 damage, etc.. and the previous bonus.
10 or more Above the DC : the creature has Advantage on the next d20 roll it makes and gains the previous bonuses.