Thank you for your question.
NJ Administrative Code 1:12-5.1 says merely the following:
(a) A party may represent himself or herself or may be represented by an attorney or a non-lawyer representative pursuant to R.1:21-1(f)(11). Representation by an attorney shall be at the party's expense. Representation by a non-lawyer representative shall comply with N.J.A.C. 1:1-5.4.
(b) In any unemployment benefits proceeding and in any State plan temporary disability and State plan family leave insurance
claim proceeding of an appeal before an appeal tribunal or the Board of Review, all fees for attorneys representing claimants shall be approved by the Board of Review after it receives submission of an authorization form and a copy of the applicable decision.
(c) The amount of fees approved for persons representing claimants shall be discretionary with the Board of Review. In determining the amount of fees, the Board of Review shall at least consider the following factors:
1. The amount of time spent on the case;
2. The complexity of the case;
3. The services performed as noted on the authorization form or any other documentation to the Board of Review; and
4. The results achieved (that is, favorable or unfavorable).
(d) The Board of Review or any appeal tribunal, in its discretion, may refuse to allow to appear before it any person who engages in misconduct at a hearing or who intentionally or repeatedly fails to observe the provisions of the Unemployment Compensation Law of New Jersey, the rules and regulations of either the Division of Unemployment Insurance
or the Division of Temporary Disability Insurance
, or the rules of the Board of Review.
So, if you are appealing a denial of benefits, you may represent yourself by filing a written appeal within the time proscribed and you need to explain in that appeal why you are entitled to the benefits and why they should not be denied in detail including your reasons and any proof as to why the termination was without good cause.
You can see: http://www.lsnjlaw.org/Jobs-Employment/Unemployment-Insurance/Appeals/Pages/Overview-Unemployment-Appeals-Process.aspx#.VWUizGbTMnU
for an explanation of the appeals process.