I want forgery ECDSA when prime p is form of 2*n+1, n is order of Elliptic curve I have parameters of an elliptic curve s.t $p=2n+1$ , when $n$ = order of elliptic curve over finite field of order prime p.

If I want to forge any message for such ECDSA, What can I do? Maybe the condition $p=2n+1$ will be helpful, but I have no idea for this.
Hasse's theorem on elliptic curves tells us that, using your notation:
$|n-p+1|\le2\sqrt{p} \Rightarrow |n-(2n+1)+1)|\le2\sqrt{2n+1}\Rightarrow n\le2\sqrt{2n+1}$ which doesn't hold for $n&gt;8$.

So either your curve is so small you can solve the ECDLP by hand or you are not defining an elliptic curve.

Could it be that the order of the curve is $2n$ but you are just working in the large prime order group (of order $n$)?
Because in that case $n$ divides $p-1=2n$ and you can mount a MOV attack.