```python
from typing import Callable, Any, Dict

class JobQueue:
    def __init__(self):
        self.jobs: Dict[str, Any] = {}
        self.job_state: Dict[str, Dict[str, int]] = {}

    def add_job(self, job_id: str, data: Any) -> None:
        self.jobs[job_id] = data
        if job_id not in self.job_state:
            self.job_state[job_id] = {'retry_count': 0, 'last_backoff': 0}

    def process_job(self, job_id: str, processor: Callable) -> bool:
        if job_id not in self.jobs:
            raise ValueError(f"Job {job_id} not found")

        if job_id not in self.job_state:
            self.job_state[job_id] = {'retry_count': 0, 'last_backoff': 0}

        # Reset tracking for the current execution attempt
        self.job_state[job_id]['retry_count'] = 0
        self.job_state[job_id]['last_backoff'] = 0

        retry_count = 0
        while retry_count <= 3:
            try:
                processor(self.jobs[job_id])
                return True
            except Exception:
                retry_count += 1
                self.job_state[job_id]['retry_count'] = retry_count

                if retry_count > 3:
                    return False

                backoff = 2 ** (retry_count - 1)
                self.job_state[job_id]['last_backoff'] = backoff
```