Binary search-like algorithm to find local peak
Why else?  The if() branch never continues.

// Why `else`
if (m==i || m==j) {
    return A[m];
}
else {
   ....

// Alternative
if (m==i || m==j) {
    return A[m];
}
... rest of code

Does the above make a difference? Easier to see code is invalid as it is missing return paths

if (A[m+1]&gt;A[m])
{
    Peak1D(A,m+1,j);
    // what happens here??? Looks like return missing
    // was return Peak1D(A,m+1,j); intended?
}
// Now do not need `else`
// else if (A[m-1]&gt;A[m])
if (A[m-1]&gt;A[m])
{
    // Peak1D(A,i,m-1);
    return Peak1D(A,i,m-1);
}
// Now do not need `else`
// else   return A[m];
return A[m];

int i,int j --> Why type int here?  Why not char or long long?  The best is to use size_t.  That is an unsigned type that is neither too narrow nor too wide for array indexing and size calculation.

// int Peak1D(int A[],int i,int j)
int Peak1D(int A[],size_t i,size_t j)

Consider more descriptive names. @Ron Beyer  How about "left" and "right"? or "starting_point" "ending_point"?

int Peak1D(int A[],size_t left,size_t right)

Code defensively.  Users of your useful code will try things not intended.  What happens when i&gt;j?  Likely bad things.  Suggest adding some tests as assert() or other error handling code.

#include &lt;assert.h&gt;

...
assert(i &lt;= j); // If assertion fails, code in debug mode exits with an error message

Use const for referenced data that is not modified.  This allows additional optimizations and allows execution with constant data.

int Peak1D(const int A[],int i,int j)

// Sample usage 
const int sample[] = { 1,2,3,4,5};
printf("%d\n",  Peak1D(sample, 0,4));

Good top of file documentation.  Suggest adding month/year or at least year.
Above all, watch functionality.  This code seems odd as I would expect (A == {6,8}, i==0, j==1) to return 8, not 6.  OTOH, comment did say local peak - Oh, well.

// correct?
if (m==i || m==j) {
   return A[m];
}

Architecture style.:  A loop could have replaced the recursive function calls.  See little value to recursion here.
Indentation style.  It is consistent, which is most important.  I find it a bit too loose, but identation is a holy war.  IMO, best to follow an automated group's coding standards.