How does a stepparent invest in their stepchild when the biological parent does everything in their power to keep them from doing so?
If the bio-parent is your spouse, this sounds like a serious marital problem and misunderstanding of how a stepfamily develops. If the bio-parent is your spouse’s ex, that may be more hopeful. If this is your spouse it could be helpful to have a conversation as to what the fear is if you do establish a relationship with the stepchild. If it’s your spouse’s ex, I would suggest a conversation between the two bio-parents so any fears (insecurities, jealousies, etc.) can be addressed and put to rest. Eventually you could initiate contact with the ex-spouse if you know it will be received.
Something else that might be helpful is counseling with someone who understands stepfamily dynamics. Otherwise, the wrong template will be laid on this situation and cause more trouble. Bottom line: your presence alone over time, can be your investment. Your attitudes and behaviors will definitely influence the stepchild. Your value will be “caught.”