Heat grill to medium-high. Make the sauce: In a large bowl, combine jam, vinegar, tomato paste, and 1 tablespoon oil. Season with salt and pepper. Set aside.
Assemble 4 long skewers, alternating 4 pork cubes with 2 onion wedges and 2 apple wedges on each (begin with pork and end with apple). Roll skewers in remaining tablespoon oil. Season with salt and pepper.
Lightly oil grates. Place skewers on grill; cover grill, and cook, turning occasionally, until grill marks are visible, 6 to 8 minutes.
Open grill; baste skewers with some sauce, and cook, turning skewers and basting occasionally with more sauce, until pork is no longer pink in the center and is nicely glazed, 4 to 8 minutes more.