Hi,
Please don't take anything personally on the work front.
Work takes up a significant percentage of your life and when you execute work with zeal you will not feel depressed. Lack of interest in doing the work leads to feelings of disappointment, bitterness, and lack of interest, leading to job dissatisfaction. Any way now that you had already submitted resignation and serving notice period where ever possible try to complete the notice period as per the terms and conditions of your employment. This will help you get proper relieving with experience certificate. However if you are very keen of getting relieved immediately please check your employment terms. If your Employer agrees for payment in lieu of notice period then for balance notice period you make proportionate amount of gross salary. This way you get relief with relieving letter as well. But please do not disclose to your current employer that you are holding a better offer.