Invalid conversion from throwing function of type (_,_,_) throws -> Void to non-throwing function type (NSData?, NSURLResponse?, NSError?) -> Void

You need to implement Do Try Catch error handling as follow:

import UIKit
import PlaygroundSupport
PlaygroundPage.current.needsIndefiniteExecution = true

extension URL {
    func asyncDownload(completion: @escaping (_ data: Data?, _ response: URLResponse?, _ error: Error?) -> ()) {
        URLSession.shared
            .dataTask(with: self, completionHandler: completion)
            .resume()
    }
}

let jsonURL = URL(string: "https://api.whitehouse.gov/v1/petitions.json?limit=100")!
let start = Date()
jsonURL.asyncDownload { data, response, error in

    print("Download ended:", Date().description(with: .current))
    print("Elapsed Time:", Date().timeIntervalSince(start), terminator: " seconds\n")
    print("Data size:", data?.count ?? "nil", terminator: " bytes\n\n")

    guard let data = data else {
        print("URLSession dataTask error:", error ?? "nil")
        return
    }

    do {
        let jsonObject = try JSONSerialization.jsonObject(with: data)
        if let dictionary = jsonObject as? [String: Any],
            let results = dictionary["results"] as? [[String: Any]] {
            DispatchQueue.main.async {
                results.forEach { print($0["body"] ?? "", terminator: "\n\n") }
      //        self.tableData = results
      //        self.Indextableview.reloadData()
            }
        }
    } catch {
        print("JSONSerialization error:", error)
    }
}
print("\nDownload started:", start.description(with: .current))