Here's a clean, production-ready refactoring that splits the monolithic file into a well-structured Python package. Each module has a single responsibility, uses relative imports correctly, and exposes a tidy public API.

### 📁 `queue/__init__.py`
```python
"""Public API for the job queue package."""

from .core import Job, JobQueue
from .priority import PriorityQueue

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

### 📁 `queue/core.py`
```python
"""Core data models and basic FIFO queue implementation."""

from dataclasses import dataclass, field
from typing import Any, Callable, Optional

@dataclass
class Job:
    """Represents a unit of work to be processed."""
    func: Callable
    args: tuple = ()
    kwargs: dict = field(default_factory=dict)
    job_id: Optional[str] = None
    priority: int = 0
    status: str = "pending"
    retry_count: int = 0
    max_retries: int = 3

class JobQueue:
    """A basic FIFO job queue."""

    def __init__(self) -> None:
        self._queue: list[Job] = []

    def add(self, job: Job) -> None:
        """Add a job to the end of the queue."""
        self._queue.append(job)

    def get_next(self) -> Optional[Job]:
        """Retrieve and remove the next job in FIFO order."""
        if not self._queue:
            return None
        return self._queue.pop(0)

    def size(self) -> int:
        """Return the number of jobs in the queue."""
        return len(self._queue)

    def process(self, job: Job) -> Any:
        """Execute a job and update its status."""
        job.status = "processing"
        try:
            result = job.func(*job.args, **job.kwargs)
            job.status = "completed"
            return result
        except Exception as e:
            job.status = "failed"
            raise e
```

### 📁 `queue/retry.py`
```python
"""Retry logic with exponential backoff."""

import time
import random
from typing import Any, Optional
from .core import Job

def process_with_retry(
    job: Job,
    base_delay: float = 1.0,
    max_delay: float = 60.0,
    max_retries: Optional[int] = None
) -> Any:
    """
    Process a job with exponential backoff retry logic.

    Args:
        job: The Job instance to process.
        base_delay: Initial delay between retries in seconds.
        max_delay: Maximum delay cap in seconds.
        max_retries: Override for job.max_retries.

    Returns:
        The result of the job function.

    Raises:
        Exception: The last exception if all retries are exhausted.
    """
    retries = max_retries if max_retries is not None else job.max_retries
    delay = base_delay

    for attempt in range(retries + 1):
        job.retry_count = attempt
        try:
            result = job.func(*job.args, **job.kwargs)
            job.status = "completed"
            return result
        except Exception as e:
            job.status = "failed"
            if attempt == retries:
                raise e

            # Exponential backoff with jitter to prevent thundering herd
            time.sleep(min(delay + random.uniform(0, 0.1 * delay), max_delay))
            delay *= 2

    raise RuntimeError("Unexpected exit from retry loop")
```

### 📁 `queue/priority.py`
```python
"""Priority queue implementation using a min-heap."""

import heapq
from typing import Optional
from .core import Job

class PriorityQueue:
    """
    A priority-based job queue where lower numeric values = higher priority.
    Uses a min-heap for O(log n) insertions and extractions.
    """

    def __init__(self) -> None:
        self._heap: list[tuple[int, int, Job]] = []
        self._counter = 0  # Stable tie-breaker for equal priorities

    def add(self, job: Job) -> None:
        """Add a job to the priority queue."""
        heapq.heappush(self._heap, (job.priority, self._counter, job))
        self._counter += 1

    def get_next(self) -> Optional[Job]:
        """Retrieve and remove the highest-priority job."""
        if not self._heap:
            return None
        _, _, job = heapq.heappop(self._heap)
        return job

    def size(self) -> int:
        """Return the number of jobs in the queue."""
        return len(self._heap)
```

### 🔑 Key Design Choices
1. **Single Responsibility**: `core.py` handles data modeling & FIFO logic, `retry.py` isolates fault tolerance, `priority.py` encapsulates ordering strategy.
2. **Relative Imports**: All inter-module imports use `.` syntax, making the package relocatable and avoiding circular dependency issues.
3. **Clean Public API**: `__init__.py` explicitly controls what users see when they `import queue`. Implementation details like `process_with_retry` remain accessible via `from queue.retry import process_with_retry`.
4. **Type Safety & Documentation**: Full type hints, docstrings, and dataclass usage improve IDE support and maintainability.
5. **Priority Queue Stability**: Uses a counter tie-breaker `(priority, counter, job)` to ensure FIFO behavior among jobs with identical priorities.

### 📦 Usage Example
```python
from queue import Job, JobQueue, PriorityQueue
from queue.retry import process_with_retry

# Basic usage
q = JobQueue()
q.add(Job(func=lambda: print("Hello")))
job = q.get_next()
if job:
    q.process(job)

# Priority usage
pq = PriorityQueue()
pq.add(Job(func=lambda: 1, priority=10))
pq.add(Job(func=lambda: 2, priority=1))
print(pq.get_next().func())  # Runs priority=1 first

# Retry usage
failing_job = Job(func=lambda: 1/0, max_retries=2)
try:
    process_with_retry(failing_job, base_delay=0.1)
except ZeroDivisionError:
    print(f"Failed after {failing_job.retry_count} attempts")
```