In a food processor, puree the peppers, lime juice and the apple cider vinegar until smooth. Transfer the mixture to a stockpot set over medium-high heat. Bring to a simmer and slowly add the sugar, whisking constantly to dissolve the sugar. Reduce heat to medium-low, add the raspberry jam and simmer for 10 minutes. Skim any scum that may appear on the top. Remove from heat and cool completely in the refrigerator. The sauce will thicken as it cools.