Creating a minimax tree recursively
Here are some things that, in addition to the other review, may help you improve your code.

Don't abuse using namespace std

Putting using namespace std at the top of every program is a bad habit that you'd do well to avoid.  In this program, especially, it's completely simply to eliminate because the namespace is already explicitly specified every place it's needed.

Prefer constexpr to old-style #define

Rather than using a #define for SIZE the code could use a constexpr:

constexpr size_t SIZE{3}; //  this is number of child nodes a node will have


It doesn't make a huge difference here, but generally the advantage is that the value has an associated type.  

Use appropriate data structures

The code implies that there are only and exactly 3 children nodes for each node, but the data structure is a std::vector&lt;Node*&gt; with a #define SIZE 3.  This means that the size is set at compile time, but that there is no explicit prohibition to having 2 or 5 or more children.  Better would be to define the variable as std::array&lt;Node*, 3&gt; v_node;.  This would also eliminate both of the resize calls associated with the v_node variable.

Be careful with signed versus unsigned

The code currently contains this line:

    for(int i = 0; i &lt; SIZE; i++){


But would it ever make sense for either i or SIZE to be negative?  Probably not, in my view, which means that it would likely make more sense, considering how they're used, to have both declared as size_t types

Prefer modern initializers for constructors

The constructor could use the more modern initializer style rather than the old style you're currently using.  Instead of this:

Tree(int s){
    size = s;
    root = new Node; 
    root-&gt;my_vec.resize(s, 36);
    root-&gt;val = 0;
    count = 0;
}


You could write this:

Tree(int s) : 
    root{new Node},
    size{s},
    count{0}
{
    root-&gt;my_vec.resize(s, 36);
    root-&gt;val = 0;
}


This could be even more simplified by implementing the following suggestion.

Rely on constructors to always create valid objects

By defining constructors for classes such as Node, you can assure that any Node object is actually valid; that is, it has a consistent internal state, according to whatever that might mean for your code.  In this particular case, defining a constructor for Node makes much of the rest of the code much simpler.  For example, we might move from a struct to a class definition like this:

class Tree;


class Node{
    std::array&lt;Node*, 3&gt; v_node;
    std::vector&lt;int&gt; my_vec;
    int val;
public:
    friend class Tree;
    Node(size_t count, size_t vecsize, int myval) :
        v_node{},
        my_vec(count, vecsize),
        val{myval}
    {}
};


Now the Tree constructor could be this:

Tree(int s) : 
    root{new Node{s, 36, 0}},
    size{s},
    count{0}
{ }


And the loop within create_tree reduces to just a few lines:

for(size_t i = 0; i &lt; SIZE; i++){
    n-&gt;v_node[i] = new Node{size-1, n-&gt;my_vec[0]-1, i};
    create_tree(n-&gt;v_node[i], size-1); 
}


This same general principle also means that it makes little sense to have separate constructor and initialization calls.  So instead of this in main:

Tree t(4);
t.ct();


It should just be this:

Tree t(4);


And the Tree constructor would be this:

Tree(int s) : 
    root{new Node{s, 36, 0}},
    size{s},
    count{0}
{ 
    create_tree(root, size);
}


The ct function would simply be eliminated.

Avoid memory leaks

You've already mentioned this in your problem statement, but for the benefit of other readers, the current version of the program leaks memory.  Two approaches would be to either add a destructor to each of the classes, or better, to convert from raw pointers to std::shared_ptr.

Algorithm correctness

Because the code is not really complete, (that is, the tree contains no meaningful data), it's difficult to say.  It constructs some tree, but whether it's a minimax tree is difficult to say outside of the context in which it will be used.