Code to modify string as per instructions
Add some comments describing your algorithm
Your code is a single function which is a bit long, and it's not very obvious what it is doing. There are two ways of dealing with this: either creating functions that implement logical steps of the algorithm individually, or add some comments to describe which steps your algorithm is doing. Don't add comments that just descibre exactly what the code does, but give a higher level description.
Unnecessary use of std::count()
You use std::count() a lot, but you don't need to. You can count the number of zeroes and ones when building window, and when you are calling window.erase() you can decrement your counts.
Consider using std::string functions to search for blocks of zeroes and ones
Instead of using std::find() and counting manually using while-loops, you can use std::string::find(). You can also construct a string directly from a subregion of another string.
auto first1 = str.find('1');
auto next0 = str.find('0', first1);
auto next1 = str.find('1', next0);

std::string window(str, first1, next1 - first1);

Once you have that, calculating the number of zeores and ones in window is easy:
auto count1 = next0 - first1;
auto count0 = window.size() - count1;

However, you might not even need the initial window:
Avoid constructing and then partially deconstructing the window
Your window consists of a number of ones followed by a number of zeroes. You are then slowly removing from the start and end until some conditions are met. However, while you are doing this, the only thing you really care about is the count of zeroes and ones, not the string window itself! You can reconstruct the final window from the counts left at the end.
Let's assume we have calculated count0 and count1 like I've written above. Then:
while (window.size() &gt; 1) {

Can be replaced with:
while (count0 + count1 &gt; 1) {

Then you do:
if (count0 &gt; count1)
    window.erase(--window.end());
else if (count1 &gt; count0)
    window.erase(window.begin());

Basically, this removes zeroes or ones until the number of zeroes or ones is equal. This can be replaced with the following:
count0 = count1 = std::min(count0, count1);

Then the next condition is:
if (str.find(&quot;10&quot;, std::distance(str.begin(), it)) == std::string::npos)
    window.erase(window.begin());
else
    window.erase(--window.end());

Since str is not modified here, you could move the if-condition outside of the loop. And the window.erase() calls can be replaced by count0-- and count1--. So what's left is:
bool has_second_10 =  str.find(&quot;10&quot;, next0 + count0) != str.npos;

while (count0 &amp;&amp; count1) {
    if (count0 != count1) {
        count0 = count1 = std::min(count0, count1);
    } else {
        if (has_second_10) {
            count0--;
        } else {
            count1--;
        }
    }
}

But wait, it gets even better: you always start with a window with both ones and zeroes, and you make the count equal, and then you remove zeroes if the original string had a second occurrence of &quot;10&quot;, otherwise you remove ones. So the single character left in the window is completely determined by has_second_10, and the while-loop can be eliminated entirely. You also don't need to count ones and zeroes anymore.
Now it's just a matter of updating the original string. Instead of modifying a character and erasing some, you can use the std::string::replace() function to do that in one go:
str.replace(first1, next1 - first1, 1, has_second_10 ? '1' : '0');

Summary
With the above improvements, the code can be simplified to:
#include &lt;iostream&gt;
#include &lt;string&gt;
 
int main() {
    int T = 0;
    std::cin &gt;&gt; T;

    while (T--) {
        int n = 0;
        std::cin &gt;&gt; n;
        std::string str;
        std::cin &gt;&gt; str;

        while (str.find(&quot;10&quot;, 0) != str.npos) {
            auto first1 = str.find('1');
            auto next0 = str.find('0', first1);
            auto next1 = str.find('1', next0); // this might be npos, but that's fine
            auto replacement = str.find(&quot;10&quot;, next1) == str.npos ? '0' : '1';
            str.replace(first1, next1 - first1, 1, replacement);
        }

        std::cout &lt;&lt; str &lt;&lt; &quot;\n&quot;;
    }
}