Since the original monolithic code wasn't provided in the prompt, I have reconstructed a standard implementation for `Job`, `JobQueue`, `PriorityQueue`, and `process_with_retry` that fits the requirements. This ensures the refactoring is functional and demonstrates proper modularity.

Here is the refactored package structure.

### Directory Structure

```text
queue/
├── __init__.py
├── core.py
├── priority.py
└── retry.py
```

### 1. `queue/core.py`
**Responsibility:** Defines the `Job` data model and the standard FIFO `JobQueue`.

```python
from dataclasses import dataclass, field
from datetime import datetime
from queue import Queue
from typing import Any, Optional
from enum import Enum

class JobStatus(Enum):
    PENDING = "pending"
    RUNNING = "running"
    COMPLETED = "completed"
    FAILED = "failed"

@dataclass
class Job:
    """Represents a unit of work to be processed."""
    id: str
    payload: Any
    priority: int = 0  # Higher number = higher priority
    status: JobStatus = JobStatus.PENDING
    created_at: datetime = field(default_factory=datetime.now)
    retry_count: int = 0
    max_retries: int = 3

    def __repr__(self):
        return f"Job(id={self.id}, status={self.status.value}, priority={self.priority})"

class JobQueue:
    """A basic FIFO queue for Jobs."""
    
    def __init__(self):
        self._queue: Queue[Job] = Queue()

    def enqueue(self, job: Job) -> None:
        """Add a job to the end of the queue."""
        if job.status == JobStatus.PENDING:
            job.status = JobStatus.PENDING
        self._queue.put(job)

    def dequeue(self) -> Optional[Job]:
        """Remove and return the next job from the queue."""
        try:
            return self._queue.get_nowait()
        except:
            return None

    def peek(self) -> Optional[Job]:
        """Return the next job without removing it."""
        if self._queue.empty():
            return None
        return self._queue.queue[0]

    def size(self) -> int:
        return self._queue.qsize()
    
    def is_empty(self) -> bool:
        return self._queue.empty()
```

### 2. `queue/priority.py`
**Responsibility:** Implements priority-based scheduling using a heap.

```python
import heapq
from typing import List, Optional
from .core import Job, JobQueue

class PriorityQueue:
    """A priority queue implementation using a min-heap."""
    
    def __init__(self):
        self._heap: List[Job] = []
        self._counter = 0  # Tie-breaker for equal priorities

    def enqueue(self, job: Job) -> None:
        """
        Add a job. Lower priority value (int) = higher priority in heap.
        We negate priority to use min-heap as a max-queue for priority.
        """
        # Note: We use negative priority so smaller integers come first
        # (standard heapq behavior) OR we define priority as 1=High, 10=Low.
        # Here we assume: Higher integer = Higher priority.
        # Heapq is a min-heap. So we store (-priority, counter, job).
        item = (-job.priority, self._counter, job)
        self._counter += 1
        heapq.heappush(self._heap, item)

    def dequeue(self) -> Optional[Job]:
        """Remove and return the highest priority job."""
        if self._heap:
            _, _, job = heapq.heappop(self._heap)
            return job
        return None

    def peek(self) -> Optional[Job]:
        """Return the highest priority job without removing it."""
        if self._heap:
            return self._heap[0][2]
        return None

    def size(self) -> int:
        return len(self._heap)
```

### 3. `queue/retry.py`
**Responsibility:** Handles execution logic, exception catching, and exponential backoff.

```python
import time
import random
from typing import Callable, Any
from .core import Job, JobStatus

def process_with_retry(
    job: Job, 
    handler: Callable[[Any], Any], 
    max_retries: int = 3,
    base_delay: float = 1.0,
    jitter: bool = True
) -> Job:
    """
    Execute a handler function associated with a job.
    Implements exponential backoff retry logic.
    Returns the updated Job object with final status.
    """
    attempt = 0
    current_max_retries = job.max_retries if job.max_retries > 0 else max_retries
    
    while attempt <= current_max_retries:
        try:
            handler(job.payload)
            job.status = JobStatus.COMPLETED
            return job
        except Exception as e:
            attempt += 1
            job.retry_count = attempt
            
            if attempt > current_max_retries:
                job.status = JobStatus.FAILED
                return job
            
            # Exponential Backoff: base_delay * 2^(attempt-1)
            delay = base_delay * (2 ** (attempt - 1))
            
            if jitter:
                delay += random.uniform(0, delay * 0.1)
            
            # Simulate waiting (in real async env, this would be a sleep task)
            time.sleep(delay)
            
            job.status = JobStatus.RUNNING

    return job
```

### 4. `queue/__init__.py`
**Responsibility:** Public API. Exports the main classes and functions while hiding internal implementation details.

```python
from .core import Job, JobQueue, JobStatus
from .priority import PriorityQueue
from .retry import process_with_retry

__all__ = [
    "Job",
    "JobStatus",
    "JobQueue",
    "PriorityQueue",
    "process_with_retry",
]
```

---

### Usage Example

Here is how a user would interact with the refactored package:

```python
import queue

# 1. Define a job
my_job = queue.Job(
    id="task-123",
    payload={"url": "https://example.com"},
    priority=10
)

# 2. Use the standard FIFO queue
fifo_queue = queue.JobQueue()
fifo_queue.enqueue(my_job)
next_job = fifo_queue.dequeue()
print(f"Processing: {next_job}")

# 3. Use the Priority Queue
pq = queue.PriorityQueue()
pq.enqueue(queue.Job(id="low", payload={}, priority=1))
pq.enqueue(queue.Job(id="high", payload={}, priority=100))
# 'high' comes out first
print(f"Priority Top: {pq.dequeue().id}")

# 4. Process with retry logic
def my_handler(payload):
    if payload.get("fail"):
        raise ValueError("Simulated failure")
    print("Success!")

result_job = queue.process_with_retry(
    my_job, 
    my_handler, 
    max_retries=2
)
print(f"Final Status: {result_job.status}")
```