Basic queue design and implementation
BUG: q_init() doesn't return a value.  Your compiler should have caught this; perhaps you're running without enough diagnostics turned on?  (I think this requires a diagnostic, so perhaps you need a better compiler).

BUG:  We forgot to copy the terminating null character!

for (int i = 0; i &lt; numtest; i++) {
    q_push(nameq, test[i], strlen(test[i]));
}


That should be strlen(test[i])+1.  This was quickly revealed by Valgrind.

Although you don't ever expect malloc() to fail, I think it's better to be in the habit of coding defensively.  &quot;Memory available&quot; might be fragmented, and not available in big enough chunks, for instance.  It's not hard to add the necessary tests, and it makes your code more re-usable, saving you much time in the longer term.
queue_t *q_init(void)
{
    queue_t *q = malloc(sizeof *q);
    if (q) {
        q-&gt;size = 0;
        q-&gt;head = q-&gt;tail = NULL;
    }
    return q;
}


bzero() isn't standard (i.e. portable) C.  Use memset() instead.  Actually, just remove that call entirely, as it's immediately followed by a memcpy() that completely overwrites it, making the bzero() a dead store.

We don't need to cast here:

    printf(&quot;[%d] %s\n&quot;, i++, (char*)h-&gt;data);




char *hname = (char*)(q_peek(nameq)-&gt;data);


data is a pointer to void, which can be assigned to any pointer type in C:
    printf(&quot;[%d] %s\n&quot;, i++, h-&gt;data);


const char *hname = q_peek(nameq)-&gt;data;


We've included &lt;stdint.h&gt; but then seemingly ignored it.  I would normally use size_t for the queue length and element sizes.  I certainly wouldn't use a signed type such as int.

Naming: why freeq() and not q_free() to match the other functions?

When pushing a value, we allocate twice, but q_pop() and freeq() don't release the value storage, only the queue node.  So we have a memory leak:
==4943== 
==4943== 21 bytes in 3 blocks are definitely lost in loss record 1 of 1
==4943==    at 0x480B77F: malloc (in /usr/lib/x86_64-linux-gnu/valgrind/vgpreload_memcheck-amd64-linux.so)
==4943==    by 0x10922B: q_push (254594.c:40)
==4943==    by 0x10942E: main (254594.c:100)

We can fix this by adding another free() before the one that releases the node object.  But a more elegant fix is to allocate just once, for the node and stored value together:
node_t *new = malloc(sizeof *new + bsize);
if (!new) {
    return ENOMEM;
}
new-&gt;next = NULL;
new-&gt;data = (char*)(new + 1);
memcpy(new-&gt;data, pdata, bsize);

We don't really need the data member any more - the value is always at the same offset from the node pointer.

The interface can be improved - users shouldn't need to know about node_t.  Instead, just return pointer to the data member.

Modified code
#include &lt;stdio.h&gt;
#include &lt;stdint.h&gt;
#include &lt;string.h&gt;
#include &lt;stdlib.h&gt;

#define MAX_QSIZE   100
#define MAX_DATSIZE 128

typedef struct node {
    struct node *next;
    char data[];               /* flexible array member */
} node_t;

typedef struct queue_t {
    node_t *head;
    node_t *tail;
    size_t size;                /* element count */
} queue_t;

queue_t *q_init(void)
{
    queue_t *q = malloc(sizeof *q);
    if (q) {
        q-&gt;size = 0;
        q-&gt;head = q-&gt;tail = NULL;
    }
    return q;
}

void *q_push(queue_t *q, const void *pdata, size_t bsize)
{
    if (!q || q-&gt;size == MAX_QSIZE || bsize &gt; MAX_DATSIZE) {
        return NULL;
    }

    node_t *new = malloc(sizeof *new + bsize);
    if (!new) {
        return NULL;
    }
    new-&gt;next = NULL;
    memcpy(&amp;new-&gt;data, pdata, bsize);

    if (q-&gt;head) {
        q-&gt;tail-&gt;next = new;
    } else {
        q-&gt;head = new;
    }
    q-&gt;tail = new;
    q-&gt;size++;

    return &amp;new-&gt;data;
}

const void *q_peek(queue_t *q)
{
    if (!q || !q-&gt;head) { return NULL; }
    return &amp;q-&gt;head-&gt;data;
}

void q_pop(queue_t *q)
{
    if (!q || !q-&gt;size) { return; }
    node_t *this = q-&gt;head;
    q-&gt;head = this-&gt;next;
    free(this);
    if (!--q-&gt;size) {
        q-&gt;tail = NULL;
    }
}

void q_free(queue_t *q)
{
    if (!q) { return; }
    node_t *h = q-&gt;head;
    while (h) {
        node_t *t = h;
        h = t-&gt;next;
        free(t);
    }
    free(q);
}


static void printq(queue_t *q)
{
    int i = 0;
    for (const node_t *h = q-&gt;head;  h;  h = h-&gt;next) {
        printf(&quot;[%d] %s\n&quot;, i++, &amp;h-&gt;data[0]);
    }
}

int main(void)
{
    const char *test[] =
    {
        &quot;January&quot;,
        &quot;February&quot;,
        &quot;Random&quot;
    };
    int numtest = sizeof test / sizeof test[0];
    queue_t *nameq = q_init();
    if (!nameq) {
        fprintf(stderr, &quot;Failed to create queue\n&quot;);
        return EXIT_FAILURE;
    }
    for (int i = 0;  i &lt; numtest;  i++) {
        if (!q_push(nameq, test[i], strlen(test[i]) + 1)) {
            fprintf(stderr, &quot;Failed to create element %i\n&quot;, i);
            return EXIT_FAILURE;
        }
    }
    printq(nameq);

    q_pop(nameq);
    printq(nameq);

    const char *hname = q_peek(nameq);
    printf(&quot;head name = %s\n&quot;, hname);

    q_free(nameq);
}

This version has no errors when compiled by gcc -std=c17 -Wall -Wextra -Wwrite-strings -Wno-parentheses -Wpedantic -Warray-bounds  -Wstrict-prototypes    -Wconversion, and no issues reported by Valgrind.