Here is the complete, production-ready refactoring. Each module follows the Single Responsibility Principle, uses proper relative imports, and exposes a clean public API.

### `queue/__init__.py`
```python
"""
queue package
Modular job queue system with priority support and retry logic.
"""
from .core import Job, JobQueue
from .priority import PriorityQueue
from .retry import process_with_retry

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

### `queue/core.py`
```python
"""Core data model and basic FIFO queue operations."""
from dataclasses import dataclass, field
from typing import Any, Optional
import threading
import time
import uuid


@dataclass
class Job:
    id: str = field(default_factory=lambda: str(uuid.uuid4()))
    name: str = ""
    payload: Any = None
    status: str = "pending"  # pending, running, completed, failed
    created_at: float = field(default_factory=time.time)
    priority: int = 0  # Higher value = higher priority


class JobQueue:
    """Thread-safe FIFO job queue."""
    
    def __init__(self) -> None:
        self._queue: list[Job] = []
        self._lock = threading.Lock()

    def enqueue(self, job: Job) -> None:
        with self._lock:
            self._queue.append(job)

    def dequeue(self) -> Optional[Job]:
        with self._lock:
            return self._queue.pop(0) if self._queue else None

    def size(self) -> int:
        with self._lock:
            return len(self._queue)

    def is_empty(self) -> bool:
        with self._lock:
            return len(self._queue) == 0
```

### `queue/priority.py`
```python
"""Priority queue implementation using a min-heap."""
import heapq
import threading
from typing import Optional
from .core import Job


class PriorityQueue:
    """Thread-safe priority queue. Higher priority values are dequeued first."""
    
    def __init__(self) -> None:
        # Heap stores tuples: (-priority, insertion_order, job)
        self._heap: list[tuple[int, int, Job]] = []
        self._counter: int = 0  # Ensures FIFO order for equal priorities
        self._lock = threading.Lock()

    def enqueue(self, job: Job) -> None:
        with self._lock:
            heapq.heappush(self._heap, (-job.priority, self._counter, job))
            self._counter += 1

    def dequeue(self) -> Optional[Job]:
        with self._lock:
            if not self._heap:
                return None
            _, _, job = heapq.heappop(self._heap)
            return job

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

    def is_empty(self) -> bool:
        with self._lock:
            return len(self._heap) == 0
```

### `queue/retry.py`
```python
"""Retry logic with exponential backoff."""
import time
import logging
from typing import Callable, Any
from .core import Job

logger = logging.getLogger(__name__)


def process_with_retry(
    job: Job,
    process_fn: Callable[[Job], Any],
    max_retries: int = 3,
    base_delay: float = 1.0,
) -> bool:
    """
    Execute a job with exponential backoff retry logic.
    
    Args:
        job: The job instance to process.
        process_fn: Callable that processes the job.
        max_retries: Maximum number of retry attempts after initial failure.
        base_delay: Initial delay in seconds before first retry.
        
    Returns:
        True if successful, False if all retries exhausted.
    """
    for attempt in range(max_retries + 1):
        try:
            job.status = "running"
            result = process_fn(job)
            job.status = "completed"
            logger.info(f"Job {job.id} completed successfully on attempt {attempt + 1}")
            return True
        except Exception as e:
            job.status = "failed"
            logger.warning(
                f"Job {job.id} failed on attempt {attempt + 1}/{max_retries + 1}: {e}"
            )
            if attempt < max_retries:
                delay = base_delay * (2 ** attempt)
                logger.info(f"Retrying in {delay:.2f} seconds...")
                time.sleep(delay)
            else:
                logger.error(f"Job {job.id} failed permanently after {max_retries + 1} attempts")
                return False
    return False
```

### Key Design Decisions:
1. **Relative Imports**: All modules use `from .core import Job` to maintain package encapsulation. This prevents circular dependencies and works correctly when the package is imported.
2. **Thread Safety**: Added `threading.Lock()` to queue operations since job queues are typically consumed/produced across threads.
3. **Stable Priority Sorting**: `PriorityQueue` uses a counter tie-breaker so jobs with equal priority maintain FIFO order (standard heap behavior).
4. **Explicit Status Tracking**: `Job.status` is updated inside `process_with_retry` to reflect lifecycle state, making debugging and monitoring easier.
5. **Clean Public API**: `__init__.py` re-exports all public components and defines `__all__` for explicit namespace control.

### Usage Example:
```python
from queue import Job, JobQueue, PriorityQueue, process_with_retry

# Basic FIFO queue
fifo = JobQueue()
fifo.enqueue(Job(name="task-1", priority=1))

# Priority queue
prio = PriorityQueue()
prio.enqueue(Job(name="low-priority", priority=1))
prio.enqueue(Job(name="high-priority", priority=10))

# Process with retry
def my_handler(job: Job):
    if job.name == "failing-task":
        raise ConnectionError("Temporary network issue")
    return "success"

job = Job(name="failing-task", priority=5)
success = process_with_retry(job, my_handler, max_retries=2, base_delay=0.5)
```