Else loop of if-else statement is not being executed even after the if condition is false. Link of question:-https://www.codechef.com/submit/FIBEASY

In a Fibonacci series, your code is too complicated:

A[0]=0;
A[1]=1;
for(m=2;m<N[i];++m)                     //fibonacci series of N terms
{
    A[m]=A[m-1]+A[m-2];

    A[m-2]=A[m-1]; // This line is suspect
    A[m-1]=A[m];   // this line too
}

In order to see what your code is doing exactly, you should learn to use the debugger, it is a great learning tool.
-----
Your code do not behave the way you expect, or you don't understand why !

There is an almost universal solution: Run your code on debugger step by step, inspect variables.
The debugger is here to show you what your code is doing and your task is to compare with what it should do.
There is no magic in the debugger, it don't know what your code is supposed to do, it don't find bugs, it just help you to by showing you what is going on. When the code don't do what is expected, you are close to a bug.
To see what your code is doing: Just set a breakpoint and see your code performing, the debugger allow you to execute lines 1 by 1 and to inspect variables as it execute.

Debugger - Wikipedia, the free encyclopedia[^]

Mastering Debugging in Visual Studio 2010 - A Beginner's Guide[^]
Basic Debugging with Visual Studio 2010 - YouTube[^]

1.11 — Debugging your program (stepping and breakpoints) | Learn C++[^]

The debugger is here to only show you what your code is doing and your task is to compare with what it should do.
-----
Learn to indent properly your code, it show its structure and it helps reading and understanding. It also helps spotting structures mistakes.

#include<iostream>
#include<vector>

using namespace std;

int main()
{
    int T,i,j,k,l;
    cin>>T;                               //no of test cases

    long int P[T];


    for(i=0;i<T;++i)
    {

        long int A[T],N[T],E,D[T],size,F[T],Z,m;
        cin>>N[i];

        A[0]=0;
        A[1]=1;
        for(m=2;m<N[i];++m)                     //fibonacci series of N terms
        {
            A[m]=A[m-1]+A[m-2];

            A[m-2]=A[m-1];
            A[m-1]=A[m];
        }

        for(m=0;m<N[i];++m)
        {                             //finding remainder of fibonacci series
            D[m]=A[m]%10;
        }

        while(1)
        {
            for(j=0;j<N[i];j+2)
            {
                if(N[i]%2==0)          //to check whether N is even or not
                {
                    for(k=0;k<(N[i]/2);++k)
                    {
                        F[k]=D[j];        //even elements  copied new array
                        D[k]=F[k];              // updating original array

                    }

                    N[i]=k;        //updating value of N to last index of new array
                }
                else
                {
                    if(N[i]==1)
                    // N[i] become 1 breaking it out of loop
                    {
                        break;
                    }
                    else                 // when N is not 1 and is odd
                    {
                        for(k=0;k<((N[i]+1)/2);++k)
                        // for odd value half value is N+1/2
                        {
                            F[k]=D[j];

                            //even elements are copied here in new array

                            D[k]=F[k];

                            // updating original array to only even indices array

                        }

                        N[i]=k;
                        //updating  N to last index of new array
                    }
                }
            }
            if(N[i]==1)
            {
                break;
            }
        }

        P[i]=F[0];            //assigning value to P
    }
    for(i=0;i<T;++i)
    {
        cout<<P[i]<<"\n";
    }
    return 0;

}

Indentation style - Wikipedia[^]

Professional programmer's editors have this feature and others ones such as parenthesis matching and syntax highlighting.
Notepad++ Home[^]
ultraedit[^]

[Update]

Quote:

this else statement is not being executed i don't know why?

Because your code is buggy, the else condition is never met.
You need to check that your code is correct at every step, it is debugging.

It is not clear what your code is expected to do and where is the (supposed) failing line.
Anyway, the following statement

for(j=0;j<N[i];j+2)

is probably wrong, because

j+2

is useless (you probably meant j+=2).

Turn on ALL compiler warnings and do read the issued ones.

[update]
You should fix your code but, first and foremost, you should really think about the problem. For instance:
You don't really need to compute the Fibonacci series, computing its reminders is just enough.
Possibly the 'odd items elimination' operation is not necessary (try with paper and pencil).
[/update]

[update 2]
Focus yourself on the D_l series. Since it contains only the reminders of the sum of previous items, it must eventually repeat itself. This observation is the key for answering the question with the original constraints (no TLE).
[/update 2]